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AB is a line segment of length 24 cm and C is its middle point. On AB, A and CB semi-circles are described. The radius of circle which touches all these semi-circles is

Solution for the question - ab is a line segment of length 24 cm and cis its middle point. on ab,aand cbsemi-circles are described. the radius of circle which t

Ab is a line segment of length 24 cm and cis its middle point-Turito

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in a <img src="data:image/png;base64,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" class="Wirisformula" alt="triangle P Q R" width="53" height="14" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#9651;«/mo»«mi»P«/mi»«mi»Q«/mi»«mi»R«/mi»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="3 sin space P plus 4 cos space Q equals 6" width="144" height="14" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«mi»sin«/mi»«mo»§#160;«/mo»«mi»P«/mi»«mo»+«/mo»«mn»4«/mn»«mi»cos«/mi»«mo»§#160;«/mo»«mi»Q«/mi»«mo»=«/mo»«mn»6«/mn»«/math»'/> and <img src="data:image/png;base64,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" class="Wirisformula" alt="4 sin space Q plus 3 cos" width="103" height="14" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»4«/mn»«mi»sin«/mi»«mo»§#160;«/mo»«mi»Q«/mi»«mo»+«/mo»«mn»3«/mn»«mi»cos«/mi»«/math»'/> p=1 then

Solution for the question - in a /_\pqr  35 lin p+4005 q=6 and 45+10+3c 05 p=1 then (pi)/(6) '/> (5pi)/(6) '/> (3pi)/(4) '/> (pi i)/(4) '/>

In a /_\pqr  35 lin p+4005 q=6 and 45+10+3c 05 p=1 th-Turito

The expression <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator tan space A over denominator 1 minus cat space A end fraction plus fraction numerator cot space A over denominator 1 minus tan space d end fraction" width="166" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»tan«/mi»«mo»§#160;«/mo»«mi»A«/mi»«/mrow»«mrow»«mn»1«/mn»«mo»§#8722;«/mo»«mi»cat«/mi»«mo»§#160;«/mo»«mi»A«/mi»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mi»cot«/mi»«mo»§#160;«/mo»«mi»A«/mi»«/mrow»«mrow»«mn»1«/mn»«mo»§#8722;«/mo»«mi»tan«/mi»«mo»§#160;«/mo»«mi»d«/mi»«/mrow»«/mfrac»«/math»'/> can be written as

Solution for the question - the expression (tan a)/(1-cot a)+(cot a)/(1-tan theta) can be writtenas sec a+cosec a '/> tan a+cot a '/> sec acos eca+1 '/> '/>

The expression (tan a)/(1-cot a)+(cot a)/(1-tan theta) can -Turito

if <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMYAAAAVCAYAAAAdMZHcAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAA8NJREFUeNrtWk9kXEEYf6JiVZSqHCKq9NBDVZSKFSuil6qKiBIVVVVlVVXvVT30Fnuo3qOn6qUqoiJKVFWsCFE5VPQS1XNuOUSs5fUbfqvbl/n3zbx5+zY7P35idzOz7/vzm/nm20mSiH5EGu2PiIiJ0Zf2PyUuMf5/CWPKiOvEZoG+yCMx7hA/E88MqDDysD/3nJwgbjmMa2Js2bBMvF+wL3wSY5G4STw7oDtGnvYrc/I2cZ/YZmxVTayyXNyAQaFwhfiKuMsYM0r8TRxy3LZdfJF6JMYz4g7x3ICWUnnbr8zJP8SrBZYdm3iYEHhPrDMT7yXE5JK8rr7wEYZ43g1iZUCFEcJ+aU5yg9SAal3xvIB63NamIewWo45z+PrC1a56QeJISyiMEPafyMk0Qxt8IU53va6gxh6XlCg7koefIn4tSUBFrfrOYo4qDnrDBl8IXCZ+Ix5p/JoqXi+grD0mfide1Iy7R1xTHD65MclDGDU88zGqkAeZz2eJe8QW/s5J5jD5LpT90pzkrgqHkgS5RlzPvCce+pZk/DDmUAXCxDwDqivr0kywzlv6YkcRdJMwFrADXcJ7j5BounHifLiiSA5OTHz9KErKA+I8dmFx1vuQWVj28UydZ9tHQnJ8F8p+aU5yhdFWvC9Kik7r6yHqfRVaJdgxTOeDFCvMNnGM4YsjhYhMwrgpKfN8/cSJiY8wPqEc0X0+K9lBVh18F8r+VihhCHwkzmA1uFByYZhatCm21yrTF/MQ3CJTGKFqfNuY+OzYh4YukWxnla3SNr4LZb+3MGRGdjCNL6hrxpehlFK1aLNzTOJsMcL0xQiEt4eyopfCsImJ746ROn7ecvBdCPutSymdoRs4aMk6PJtYhdc048tw+Fa1aGVzVGFPheGLDl4Qf/RQGLYx8RXGQU47ho3vQthvffjWOUTVonyNA2OCjsRbTd3X6KEwdC1a1RxTqIcrlr4wnROKEoZtTHyFsWxxxpiTlE0rDr4LYb80J03CyN5JkR1aJ1HLdeONpGVn6gQVIQxdi1Y3Rw2BrDAO8I/R0eqFMDgx8RWG6NyJFu1dJPR4xseTqPE7PyRP4HXNwXch7Lf+gc90J2Ur+Xe/pIKSQtZNWE/+b8mFvhJicyaxFaZs7Exysj3Y7YvuZ2jD/rEeCIMTk7wgFolt2L0r2SFEF+oXdoGf2DFU8dP5Lm/7WTlpupNy2i4R+qDIS4QR+YOVkzZ3Up4kvKsdDcfOSD+A64uIcoCdk0XfyYmI6AvY3kmJiBhYYQjo7qRERJwa/AXuRG2EWq7FggAAAeR0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1Yj48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+ZjwvbWk+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPms8L21pPjwvbXN1Yj48bW8+KDwvbW8+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPng8L21pPjxtbz4pPC9tbz48bW8+PTwvbW8+PG1uPjE8L21uPjxtbz4vPC9tbz48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+azwvbWk+PG1vPig8L21vPjxtc3VwPjxtaT5zaW48L21pPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj5rPC9taT48L21zdXA+PG1vPiYjeEEwOzwvbW8+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPng8L21pPjxtbz4rPC9tbz48bXN1cD48bWk+Y29zPC9taT48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+azwvbWk+PC9tc3VwPjxtbz4mI3hBMDs8L21vPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj54PC9taT48bW8+KTwvbW8+PC9tYXRoPsM65psAAAAASUVORK5CYII=" class="Wirisformula" alt="straight f subscript straight k left parenthesis straight x right parenthesis equals 1 divided by straight k left parenthesis sin to the power of straight k space straight x plus cos to the power of straight k space straight x right parenthesis" width="198" height="21" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨normal¨»f«/mi»«mi mathvariant=¨normal¨»k«/mi»«/msub»«mo»(«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»)«/mo»«mo»=«/mo»«mn»1«/mn»«mo»/«/mo»«mi mathvariant=¨normal¨»k«/mi»«mo»(«/mo»«msup»«mi»sin«/mi»«mi mathvariant=¨normal¨»k«/mi»«/msup»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»+«/mo»«msup»«mi»cos«/mi»«mi mathvariant=¨normal¨»k«/mi»«/msup»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»)«/mo»«/math»'/> where <img src="data:image/png;base64,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" class="Wirisformula" alt="straight x element of straight R comma straight k greater or equal than 1" width="76" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»x«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»R«/mi»«mo»,«/mo»«mi mathvariant=¨normal¨»k«/mi»«mo»§#8805;«/mo»«mn»1«/mn»«/math»'/> then <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGYAAAATCAYAAABiMHgQAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAAdVJREFUeNpjYKAOyALiDhLUd0D1DEYwbPyiB8THydB3FKp31C8EgAcQ3wXiP0D8n0RHGZBhnzEQHx71C2HwEIi1SNRjAPUMueAw1FOjfsED/pOhpwuIcyiwM4/E8nzE+eU/GiYW7ABiWyQ+B7SMlkZTJwrEZ6DyyMASiPeO+oX6qewTELOhiekA8TY0sS1A7IZFPxvUjOHul/9EYKp65g8O8RykJmQ8EC/GY8avQRIxg9UvVPUMCKwCYnto60iYDM9QksoGm18GRfaHAVuoQ9Pw6B/sRRm1/ELToiwai5rdQGyNRS0TtPkYDS2TcQFaVZi4/GIOxAeB+AeWABmsfsEbMTrQNv5/IpuYjUCcCGXHAvEEPOV3F538AurXnIP6hZTm8kD7BWfECCI1G/8T0SkzhZbJyKAP6il6dcqw+WUhWnOYYYj4BWfErIFmU1xqjiONE3FAiwRBLOq2IZlD62EMbO58DS2OQKMCt4A4dIj4BSsoR0sd2Dw8VAYxQa2u2UDMB62oZyMVUUPNL0S3IDJIHI7oItDCoQW4Ba3IYYAHmnuGol+o0gwdLGA2WrHEBh1aGRZgKEeMHrQBACrKWIB4CgNkemA0YgYBiIb23l/iqPwHDQAArLfAQ2QopcAAAAEsdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdWI+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPmY8L21pPjxtbj40PC9tbj48L21zdWI+PG1vPig8L21vPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj54PC9taT48bW8+KTwvbW8+PG1vPiYjeDIyMTI7PC9tbz48bXN1Yj48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+ZjwvbWk+PG1uPjY8L21uPjwvbXN1Yj48bW8+KDwvbW8+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPng8L21pPjxtbz4pPC9tbz48bW8+PTwvbW8+PC9tYXRoPqwZ5D4AAAAASUVORK5CYII=" class="Wirisformula" alt="straight f subscript 4 left parenthesis straight x right parenthesis minus straight f subscript 6 left parenthesis straight x right parenthesis equals" width="102" height="19" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨normal¨»f«/mi»«mn»4«/mn»«/msub»«mo»(«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»)«/mo»«mo»§#8722;«/mo»«msub»«mi mathvariant=¨normal¨»f«/mi»«mn»6«/mn»«/msub»«mo»(«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»)«/mo»«mo»=«/mo»«/math»'/>

Solution for the question - if f_(k)(x)=1//k(sin^(k)x+cos^(k)x) where x in r,k >= 1 thenf_(4)(x)-f_(6)(x)= (1)/(12) '/> (1)/(9) '/> (1)/(3) '/> (1)/(6) '/>

If f_(k)(x)=1//k(sin^(k)x+cos^(k)x) where x in r,k >= 1 -Turito

Step by step solution: Given that, <img src="data:image/png;base64,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" class="Wirisformula" alt="theta subscript 1 equals 25 degree" width="62" height="18" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»§#952;«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»25«/mn»«mo»§#176;«/mo»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="theta subscript 2 equals 75 degree" width="62" height="18" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»§#952;«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»75«/mn»«mo»§#176;«/mo»«/math»'/> It is also given that <img src="data:image/png;base64,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" class="Wirisformula" alt="s subscript 1 equals s subscript 2" width="51" height="14" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»s«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«msub»«mi»s«/mi»«mn»2«/mn»«/msub»«/math»'/> We know that <img src="data:image/png;base64,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" class="Wirisformula" alt="s equals R theta" width="47" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»s«/mi»«mo»=«/mo»«mi»R«/mi»«mi»§#952;«/mi»«/math»'/> <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEwAAAARCAYAAAB3h0oCAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAZ9JREFUeNpjYBg64AcQ/wfip0B8Eoi3AbEomWZZA/E6qFkHgdicYZgBFSC+gCbWCsRdZJhlDg0sJigfFOh3h1uABQDxUjSxcCCeT4ZZoICXRhPbAcR65DisGogfAvEfaPIvHyQBVg/EJWhijUBcQKI5LjgCeTkQe5ETWLOBmI0KHvxPBCYFrAJiPyQ+HxDfAGJxEs0B+S8Iizgoi7qR6smj0BgYjOAWEEsCMQsQewDxOSAOJcOca3gikNTABzvgHFpMDgbAhFREwLAtmeZ8IkGcKACKxcNAvB+IeQZJljSHugcGLMmsHUEpaC8WcVMgXkNJjHIA8SUgjsUipwbEtViqeFqCSCwF9W4glifRfbDmBLYKJZFSv84F4mgs4ouBOI2MQpsSMAlqJwNaKltIovt4sHheEFoMsVHiV1No4ShMIMvRC6zDUeWDspcWie67AsR5ULYGEB8HYh8iihcM8AEq8QdaXmiQYwiNwDtoMcGAJZVtI9F9etBU9gta7BBTwVHFr/QMsIF232iAjQbYaIANnwCjtE9Ij4CilvuwmgUA6xSHH0suzR0AAADBdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdWI+PG1pPnM8L21pPjxtbj4xPC9tbj48L21zdWI+PG1vPj08L21vPjxtbz4mI3hBMDs8L21vPjxtc3ViPjxtaT5SPC9taT48bW4+MTwvbW4+PC9tc3ViPjxtc3ViPjxtaT4mI3gzQjg7PC9taT48bW4+MTwvbW4+PC9tc3ViPjwvbWF0aD4AQ1yKAAAAAElFTkSuQmCC" class="Wirisformula" alt="s subscript 1 equals space R subscript 1 theta subscript 1" width="76" height="17" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»s«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mo»§#160;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«msub»«mi»§#952;«/mi»«mn»1«/mn»«/msub»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="s subscript 2 equals R subscript 2 theta subscript 2" width="72" height="17" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»s«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«msub»«mi»§#952;«/mi»«mn»2«/mn»«/msub»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="s subscript 1 equals s subscript 2" width="51" height="14" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»s«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«msub»«mi»s«/mi»«mn»2«/mn»«/msub»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="rightwards double arrow R subscript 1 space end subscript left parenthesis 25 degree right parenthesis equals R subscript 2 left parenthesis 75 degree right parenthesis" width="150" height="19" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8658;«/mo»«msub»«mi»R«/mi»«mrow»«mn»1«/mn»«mo»§#160;«/mo»«/mrow»«/msub»«mo»(«/mo»«mn»25«/mn»«mo»§#176;«/mo»«mo»)«/mo»«mo»=«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mo»(«/mo»«mn»75«/mn»«mo»§#176;«/mo»«mo»)«/mo»«/math»'/> <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC8AAAAsCAYAAAD1s+ECAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAAAVtJREFUeNpjYKA/+AHE/4H4KRCfBOJtQCzKMASAChBfQBNrBeKuoeD4ACBeiiYWDsTzh4Lj64G4BE2sEYgLhoLjVwGxHxKfD4hvALH4UHD8LSCWBGIWIPYA4nNAHDoUHM4ExH+gJQ0M2zIMEWAOxPuR+JZDpZQBgUgspcpuIJbHolYNiGuxFKsDBiYBcRqaGCj0F2JRuxiq9v9gcfw6IPbCIr4XiLVw6Bk0jn8HxBxYxC2hTYRB7XhywKjjRx0/Uhz/Hwse2aAE2hIckqAaiB8CsfVQSm/YcCu0pTjkwFyoB5ZSIRDIwRRb2jHUQn7Qp3lCpQ0PwygYBXQHo8N9AwFGh/sGCowO9w0EGB3uGyhA7HAfLFZ+AfFRaPE64ICU4T5YMsuC5osBB+QM98Fq5AEH5Az32QPxwaHYBpKEpnmloeZw0Pj8FqgHhlyIbxuqQywgh2sM1fY+0aMFAGlbiGhuaulVAAAAoXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4mI3gyMUQyOzwvbW8+PG1mcmFjPjxtc3ViPjxtaT5SPC9taT48bW4+MTwvbW4+PC9tc3ViPjxtc3ViPjxtaT5SPC9taT48bW4+MjwvbW4+PC9tc3ViPjwvbWZyYWM+PC9tYXRoPuoV2HUAAAAASUVORK5CYII=" class="Wirisformula" alt="rightwards double arrow R subscript 1 over R subscript 2" width="47" height="44" style="vertical-align:-17px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8658;«/mo»«mfrac»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«/mfrac»«/math»'/><img src="data:image/png;base64,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" class="Wirisformula" alt="equals 3 over 1" width="35" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«mfrac»«mn»3«/mn»«mn»1«/mn»«/mfrac»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="rightwards double arrow R subscript 1 colon R subscript 2 equals 3 colon 1" width="107" height="17" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8658;«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»:«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»3«/mn»«mo»:«/mo»«mn»1«/mn»«/math»'/> (answer) Hence, option(b) is the correct option.

Two arcs of same length of two different circles subtended angles of  <img src="data:image/png;base64,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" class="Wirisformula" alt="25 to the power of ring operator" width="32" height="16" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mn»25«/mn»«mo»§#8728;«/mo»«/msup»«/math»'/> and <img src="data:image/png;base64,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" class="Wirisformula" alt="75 to the power of ring operator" width="32" height="16" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mn»75«/mn»«mo»§#8728;«/mo»«/msup»«/math»'/>  at their centers respectively. Then the ratio of the radii of the circles is

Solution for the question - two arcs of same length of two different circles subtended angles of25^(@) and 75^(@) at their centers respectively. then the ratio

Two arcs of same length of two different circles subtended angl-Turito

Let <img src="data:image/png;base64,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" class="Wirisformula" alt="theta element of left parenthesis 0 comma pi divided by 4 right parenthesis" width="86" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#952;«/mi»«mo»§#8712;«/mo»«mo»(«/mo»«mn»0«/mn»«mo»,«/mo»«mi»§#960;«/mi»«mo»/«/mo»«mn»4«/mn»«mo»)«/mo»«/math»'/> and <img src="data:image/png;base64,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" class="Wirisformula" alt="straight t subscript 1 equals left parenthesis tan space theta right parenthesis to the power of me theta end exponent comma straight t subscript 2 equals left parenthesis tan space theta right parenthesis to the power of cot space theta end exponent comma straight t subscript 3 equals left parenthesis cot space theta right parenthesis to the power of con space theta end exponent straight t subscript 4 equals left parenthesis cot space theta right parenthesis to the power of cos space theta end exponent" width="447" height="20" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨normal¨»t«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mo»(«/mo»«mi»tan«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«msup»«mo»)«/mo»«mrow»«mi»me«/mi»«mi»§#952;«/mi»«/mrow»«/msup»«mo»,«/mo»«msub»«mi mathvariant=¨normal¨»t«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mo»(«/mo»«mi»tan«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«msup»«mo»)«/mo»«mrow»«mi»cot«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«/mrow»«/msup»«mo»,«/mo»«msub»«mi mathvariant=¨normal¨»t«/mi»«mn»3«/mn»«/msub»«mo»=«/mo»«mo»(«/mo»«mi»cot«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«msup»«mo»)«/mo»«mrow»«mi»con«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«/mrow»«/msup»«msub»«mi mathvariant=¨normal¨»t«/mi»«mn»4«/mn»«/msub»«mo»=«/mo»«mo»(«/mo»«mi»cot«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«msup»«mo»)«/mo»«mrow»«mi»cos«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«/mrow»«/msup»«/math»'/> then

Solution for the question - let theta in(0,pi//4) and t_(1)=(tan theta)^(me theta)t_(2)=(tantheta)^(k+t)theta_(3)t_(3)=(cot theta)^(con theta)t_(4)=(cot theta)^

Let theta in(0,pi//4) and t_(1)=(tan theta)^(me theta)t_(-Turito

Step by step solution: Given, <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAOCAYAAABjLjEIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAANvpXuIwAAAeRJREFUeNrtljFIQlEUhkUkJCSQEGkQQRykNSIkoiUaJMSlQaJJcGhyCCKiISKIxraIhoYWiWiQ1hBpaBGJiNYGh3ARkZAQ7L/0P7hcrk/vk+eiP3z43r3nvnc875xzr8czlao90AYtXk+UVsE9//wvqIEdjZ2Yj4AYrydKZZAFAd4vgheOyRJZFAfRSQySTiIQb8pYHjQZoLy6wAtOwLeUjlEXHTwCX6ALeuBAmQ+zPDq0W9c8Q2TFBajT5wcQNPSjY2JcApd8iQhYEWRs7HtDYBegazDTZ36OXzgtlca7JkBVcEZ78ax9sGXwn5MsuaGUZVBk3YKUS1kkHNuwmRfZcaj5iHJQz/lRncoPXtnQh9Izo6o2OrfKbZtZkNbMedkTQspYi7/WfcNBaVkS6x7BpsmiH8kBy4n2gDWjlJvQAqjwAwWk8ZU+z5LLYplrnSjGAMVNFzY0Z4rqGHYXP3vPrjSW1pS+qhSbtKkS7IWzTpyt02FLx9xZxqEb5VCXZK+w0xL4NHxPmMH3OXX0FFyxzEQfugNPYwiQKJsPMK+Mi7EC/Qmyia8pNjXubD7uboUBTbjETBr53FJkFvl5Xsq4EJgme0yX/SjRp29UaCMCltPYRLi5dFmyuRF6qGOFpgfyf/0B/HF7/FxGNwUAAACZdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPmE8L21pPjxtbz49PC9tbz48bWk+czwvbWk+PG1pPmU8L21pPjxtaT5jPC9taT48bW8+JiN4QTA7PC9tbz48bW4+MjwvbW4+PG1vPiYjeEIwOzwvbW8+PC9tYXRoPr7wjCYAAAAASUVORK5CYII=" class="Wirisformula" alt="a equals s e c space 2 degree" width="73" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»=«/mo»«mi»s«/mi»«mi»e«/mi»«mi»c«/mi»«mo»§#160;«/mo»«mn»2«/mn»«mo»§#176;«/mo»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="b equals s e c space 2" width="68" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»b«/mi»«mo»=«/mo»«mi»s«/mi»«mi»e«/mi»«mi»c«/mi»«mo»§#160;«/mo»«mn»2«/mn»«/math»'/> Now, <img src="data:image/png;base64,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" class="Wirisformula" alt="a equals space s e c space 2 degree space equals space" width="102" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»=«/mo»«mo»§#160;«/mo»«mi»s«/mi»«mi»e«/mi»«mi»c«/mi»«mo»§#160;«/mo»«mn»2«/mn»«mo»§#176;«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«/math»'/><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKIAAAAjCAYAAAAXHtFmAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAA+NJREFUeNrtXFFkXEEUHbFWVJSoqqgqVRX9iBAVKyJCRa2KClEVVRWiKiofpSL6WSJflY+yqvpfEVUVpWqtiCgVERXVn8pHPqJUrKgVj/Te5qw8k3n75r2VNy+793DEzs7embl7371z78xGqfShj7hALBP3ievEMSUQJIwS8R6xDa+vE1fQJhA4xWXihqhBkAZURAUC18ghPAsEztBK/IokRiBwgnbie+KQqELgCldghFdFFQJX6CS+Jp4RVQhc4QLxHTHTpOt/TJxt8DXOYp2pxkd4xGZEF3G1Sda6gvWmFgc12AxfTrfWdpb4CpUDZgFttriBCMNHplyL/UAc8L0/SFwi/sX7P4kviediyrPt10Nclg1A+tCtzLXSL8Rh3+vbaLPBBAzgms+oxzQDKBJHiFltLp9iyovSbxkGKUgR5oiTWtsocd7Qlz1W2Nk7n9F/q2M+5Zjyooz7JGg/PEPcInoIhc8MicQCXO1WgEtug1K31eHtmUV1WA88bUhaF+yB+rU2lm+qoQ7ivVooqPgXRbh09iOmvCjj5kzefQYlk2zAh9i9bvjCBFv+d4Pi14gv0J9lPUU4SdNeM2zP6UIXZcN4fwLmwG07IetnQ+qIUbF4iH1iPqa8KONmDZ73//7kZkjomDZkuFktLZ9vkKQhaV14lm1V7IfIq2CPtohEZB8hc8zioZ2qQ16UcY3rGMUTPGzo3ELcJZ7X2sr4W339O0YYPqiTJwEXuohqiBULva7Bs2Uwpz54u6AaHs/3DrLzgZjyoo5rfKA6kMkU1dHFVEZvgBGsaOl6mtLxeo04aV2YQvNOQGhutQjNLO9iQHa+HfLZNhhjHHlRxjWGZv8ief9z39c2jJpQLeThjhsJSeriszp+w4gTkluGvkMWycqSz0NHDesmj2srL8q4ubBS1BstpucMT4iOHkOm1QhIShem8s0IkiYdby0yUw6Ddw3tnRbz70IojSMvyriTWLcRHFY21fHK+iY2sS3YS0wbyg3ryBIzyBSn1Om+R5ikLoIK2kV8NoNQxhl9qcZWxB/2uN+4Ojq374WH9ydiJeyJq/s5Lg39Ij4whFEbebb9lDIUtHexCA8L7wyoLS2jzyYG0nEJk/Aw8PgpND6XulhVx89f2+GVK8hCC9qeNcgQFRIq9qh7mEfJ8MD0I+OvgMUaJSYbebb95IgvxZBLD4LU4JFq/GtgvC+ckK9aIAhBOzb5nmru62ACx+jxZZq6wcnvmgVOIIYoEEMUCIIM0ROVCFzACzFMgeDE0WIIxXyqkBXVCJIE/xu6Pa2NTxyeq8Pb0AJBIuAbHPqvyPLwinOinsbDP34JarFvQ6/xAAABFnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5zPC9taT48bWk+ZTwvbWk+PG1pPmM8L21pPjxtbz4mI3hBMDs8L21vPjxtZnJhYz48bW4+MjwvbW4+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPiYjeDNDMDs8L21pPjwvbWZyYWM+PG1vPj08L21vPjxtaT5zPC9taT48bWk+ZTwvbWk+PG1pPmM8L21pPjxtbz4mI3hBMDs8L21vPjxtbz4oPC9tbz48bW4+MDwvbW4+PG1vPi48L21vPjxtbj42MzY2PC9tbj48bW8+KTwvbW8+PC9tYXRoPr/9gvAAAAAASUVORK5CYII=" class="Wirisformula" alt="s e c space 2 over straight pi equals s e c space left parenthesis 0.6366 right parenthesis" width="162" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»s«/mi»«mi»e«/mi»«mi»c«/mi»«mo»§#160;«/mo»«mfrac»«mn»2«/mn»«mi mathvariant=¨normal¨»§#960;«/mi»«/mfrac»«mo»=«/mo»«mi»s«/mi»«mi»e«/mi»«mi»c«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mn»0«/mn»«mo».«/mo»«mn»6366«/mn»«mo»)«/mo»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="b equals s e c space 2" width="68" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»b«/mi»«mo»=«/mo»«mi»s«/mi»«mi»e«/mi»«mi»c«/mi»«mo»§#160;«/mo»«mn»2«/mn»«/math»'/> Now, sec x is an increasing function in the range <img src="data:image/png;base64,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" class="Wirisformula" alt="left square bracket 0 comma straight pi over 4 right parenthesis" width="45" height="31" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»[«/mo»«mn»0«/mn»«mo»,«/mo»«mfrac»«mi mathvariant=¨normal¨»§#960;«/mi»«mn»4«/mn»«/mfrac»«mo»)«/mo»«/math»'/> Thus, <img src="data:image/png;base64,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" class="Wirisformula" alt="s e c left parenthesis 0.6366 right parenthesis less than s e c 2" width="143" height="16" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»s«/mi»«mi»e«/mi»«mi»c«/mi»«mo»(«/mo»«mn»0«/mn»«mo».«/mo»«mn»6366«/mn»«mo»)«/mo»«mo»§#60;«/mo»«mi»s«/mi»«mi»e«/mi»«mi»c«/mi»«mn»2«/mn»«/math»'/> <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHoAAAAOCAYAAADg6ggzAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAANvpXuIwAAAfVJREFUeNrtVzFIAlEYFhGJCEEipEECcZDWiDhEWqIhwq0hpElwaJIQIpoDaWyNxpaIaHANEWlwCYmI1oamFpEGiQP7f/iE1+POe+9Oh3v6wYfne/8777v/f9/7jURmE8fEH2If13OEDHniPRL4S+wSSw5xPJ8mZnA9K7qNQYt4SFzC93XiM8ZE8G7OEtcMSbSqbqPByXyVxirEHpJc8bF7WiHVrYwaMaERf078JNrEIfFUmk/BcgaI23a4B1fpJfELtvRATGo+92BC9sgJfiJapuseCcgrxl4T4y7zCVRcUbCbNwexL8QLxMdRbPsaz2zBxvzC0khwqHQPFckPER1zH/6RnTHzXK1n0lhDekF14lWAJC0QO4qFGTTBpuj+hxsk+3ZMzAGqsugwF8UZuSKN9YXi4c9vH3Y1Aq97JO76XM/6TnysC41u1R1d99jRjFVim9gUOkLGlss9RavZxFo/yEBsNqBlN0FLc22YdWuf0aKN8Jl0JIxxtd95rNtDA6KLHM7IxQl1ryML1014qHXXpArVsfqS9PI6Hms2iB+av5PCi4xN4e9KQdil1gzpVgZb0TtxWRrnsSrsP4kGpSDFdNH0xdB9Vj3cpIHKniYKitZqmm5H9HD22NgBOZfzpI0YFl92iEnDNm3YYDlAfzHXPYf5+ANNrcsCpE/+YgAAANp0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjFEMjs8L21vPjxtaT5zPC9taT48bWk+ZTwvbWk+PG1pPmM8L21pPjxtbz4mI3hBMDs8L21vPjxtbj4yPC9tbj48bW8+JiN4QjA7PC9tbz48bW8+Jmx0OzwvbW8+PG1pPnM8L21pPjxtaT5lPC9taT48bWk+YzwvbWk+PG1vPiYjeEEwOzwvbW8+PG1uPjI8L21uPjwvbWF0aD5UPjXRAAAAAElFTkSuQmCC" class="Wirisformula" alt="rightwards double arrow s e c space 2 degree less than s e c space 2" width="122" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8658;«/mo»«mi»s«/mi»«mi»e«/mi»«mi»c«/mi»«mo»§#160;«/mo»«mn»2«/mn»«mo»§#176;«/mo»«mo»§#60;«/mo»«mi»s«/mi»«mi»e«/mi»«mi»c«/mi»«mo»§#160;«/mo»«mn»2«/mn»«/math»'/> <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADkAAAANCAYAAAAT88Y+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAUpJREFUeNpjYBge4BsQMzEMY6ACxJeGuiesgfggHvkAIF5OTQtLgJiPSLWg5NMIxC+B+BcQXwBieTI8txeILfGoqwfiaqhdz4H4BxDvB2JJcj0JMuwh1AGEwBYgngTEglAPr4KGOiFgSaTnYABk7l0gLkeyq49Q7P4nErfiyeyRUMuRwUIg9qKi52DgFhBroYmBUtsnSpPtXKhHl+KQ34/FoQcJJFeQeUUkuoMJWrKiAw5CniQ2JjvwxCR6kQ5ifyEime7HEUC4gDlUPTaz9tI6T77GUoicI9IOWLIlxrOgbDEfizgoRdRSUrryEKHuKTTJwADIwjUk2mULxIcJeBZUsCWiibFB601JBhqDZiCeCU2m8tC8u41Ms2CexQbWQQseFyhfGiqWSK9KvBpawtZCY/UlkVUIKQBkph/Uo3+gdXEAwwAC0YGyGADs7lqr94pT0gAAAHF0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjFEMjs8L21vPjxtaT5hPC9taT48bW8+Jmx0OzwvbW8+PG1pPmI8L21pPjwvbWF0aD7DqCbMAAAAAElFTkSuQmCC" class="Wirisformula" alt="rightwards double arrow a less than b" width="57" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8658;«/mo»«mi»a«/mi»«mo»§#60;«/mo»«mi»b«/mi»«/math»'/> Hence, option(b) is the correct option.

Solution for the question - a=sec 2^(@),b=sec 2=> 2a=bb<aa<ba=b

A=sec 2^(@),b=sec 2=> -Turito

Step by step solution: Given, <img src="data:image/png;base64,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" class="Wirisformula" alt="x equals space cos space 1 degree" width="78" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mo»§#160;«/mo»«mi»cos«/mi»«mo»§#160;«/mo»«mn»1«/mn»«mo»§#176;«/mo»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="y equals space cos 1" width="66" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mo»§#160;«/mo»«mi»cos«/mi»«mn»1«/mn»«/math»'/> Now, <img src="data:image/png;base64,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" class="Wirisformula" alt="x equals cos space 1 degree equals cos" width="117" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mi»cos«/mi»«mo»§#160;«/mo»«mn»1«/mn»«mo»§#176;«/mo»«mo»=«/mo»«mi»cos«/mi»«/math»'/><img src="data:image/png;base64,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" class="Wirisformula" alt="1 over straight pi equals cos left parenthesis 0.3183 right parenthesis" width="128" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mi mathvariant=¨normal¨»§#960;«/mi»«/mfrac»«mo»=«/mo»«mi»cos«/mi»«mo»(«/mo»«mn»0«/mn»«mo».«/mo»«mn»3183«/mn»«mo»)«/mo»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="y equals space cos space 1" width="70" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mo»§#160;«/mo»«mi»cos«/mi»«mo»§#160;«/mo»«mn»1«/mn»«/math»'/> Now, cos x is a decreasing function in the range <img src="data:image/png;base64,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" class="Wirisformula" alt="left square bracket 0 comma straight pi right square bracket" width="37" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»[«/mo»«mn»0«/mn»«mo»,«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«mo»]«/mo»«/math»'/> Thus, <img src="data:image/png;base64,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" class="Wirisformula" alt="cos left parenthesis 0.3183 right parenthesis greater than cos space 1" width="147" height="16" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»cos«/mi»«mo»(«/mo»«mn»0«/mn»«mo».«/mo»«mn»3183«/mn»«mo»)«/mo»«mo»§#62;«/mo»«mi»cos«/mi»«mo»§#160;«/mo»«mn»1«/mn»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="rightwards double arrow cos space 1 degree space greater than space cos space 1" width="130" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8658;«/mo»«mi»cos«/mi»«mo»§#160;«/mo»«mn»1«/mn»«mo»§#176;«/mo»«mo»§#160;«/mo»«mo»§#62;«/mo»«mo»§#160;«/mo»«mi»cos«/mi»«mo»§#160;«/mo»«mn»1«/mn»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="rightwards double arrow x greater than y" width="56" height="13" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8658;«/mo»«mi»x«/mi»«mo»§#62;«/mo»«mi»y«/mi»«/math»'/> Hence, option(d) is the correct option.

I<img src="data:image/png;base64,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" class="Wirisformula" alt="x equals cos invisible function application 1 to the power of ring operator comma y equals cos invisible function application 1 not stretchy rightwards double arrow" width="163" height="18" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mi»cos«/mi»«mo»§#8289;«/mo»«msup»«mn»1«/mn»«mo»§#8728;«/mo»«/msup»«mo»,«/mo»«mi»y«/mi»«mo»=«/mo»«mi»cos«/mi»«mo»§#8289;«/mo»«mn»1«/mn»«mo stretchy=¨false¨»§#8658;«/mo»«/math»'/>

Solution for the question - i x=[051^(@),y=[051=>:} 2x=yx yx=y

I x=[051^(@),y=[051=>:} -Turito

If ABCD is a cynic quadrilateral such that 12 tan <img src="data:image/png;base64,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" class="Wirisformula" alt="A minus 5 equals 0" width="66" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»-«/mo»«mn»5«/mn»«mo»=«/mo»«mn»0«/mn»«/math»'/> and 5cos B+3=0, then cos C tan D=

Solution for the question - if abcd is a cynic quadrilateral such that 12 tan a-5=0 and 5cos b+3=0,then cos c tan d= (23)/(16) '/> (-13)/(16) '/> (16)/(13) '/> '/>

If abcd is a cynic quadrilateral such that 12 tan a-5=0 and-Turito

<img src="data:image/png;base64,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" class="Wirisformula" alt="integral fraction numerator d x over denominator square root of x squared plus 2 x plus 1 end root end fraction" width="124" height="46" style="vertical-align:-23px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8747;«/mo»«mfrac»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«msqrt»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/msqrt»«/mfrac»«/math»'/> = A log |x + 1| + C for x &lt; – 1 then A is -

Solution for the question - int(dx)/(sqrt(x^(2)+2x+1)) = a log |x + 1| + c for x < 1 then a is - none-110

Int(dx)/(sqrt(x^(2)+2x+1)) = a log |x + 1| + c for x < 1 -Turito

Solution for the question - cos a,5 in a,cot a are in then tan^(6)a-t^(2)m^(2)quad a= 210-1

Cos a,5 in a,cot a are in then tan^(6)a-t^(2)m^(2)quad a= -Turito

Solution for the question - f(x)=x^(3)-2x^(2)+3x-5=>f[sin((5pi)/(2))]+f[sin((3pi)/(2))]= -1414-1010

F(x)=x^(3)-2x^(2)+3x-5=>f[sin((5pi)/(2))]+f[sin((3pi)/(2))]= -Turito

If cos <img src="data:image/png;base64,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" class="Wirisformula" alt="theta equals 3 over 5" width="46" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#952;«/mi»«mo»=«/mo»«mfrac»«mn»3«/mn»«mn»5«/mn»«/mfrac»«/math»'/> and <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=" class="Wirisformula" alt="theta" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#952;«/mi»«/math»'/> is not in the first quadrant, then <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator 5 tan space left parenthesis pi plus theta right parenthesis plus 4 cos space left parenthesis pi plus theta right parenthesis over denominator secc space left parenthesis 2 pi minus theta right parenthesis minus 4 cot space left parenthesis 2 pi plus theta right parenthesis end fraction equals" width="239" height="39" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»5«/mn»«mi»tan«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mi»§#960;«/mi»«mo»+«/mo»«mi»§#952;«/mi»«mo»)«/mo»«mo»+«/mo»«mn»4«/mn»«mi»cos«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mi»§#960;«/mi»«mo»+«/mo»«mi»§#952;«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»secc«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mn»2«/mn»«mi»§#960;«/mi»«mo»§#8722;«/mo»«mi»§#952;«/mi»«mo»)«/mo»«mo»§#8722;«/mo»«mn»4«/mn»«mi»cot«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mn»2«/mn»«mi»§#960;«/mi»«mo»+«/mo»«mi»§#952;«/mi»«mo»)«/mo»«/mrow»«/mfrac»«mo»=«/mo»«/math»'/>

Solution for the question - if cos theta=(3)/(5) and theta is not in the first quadrant, then(5tan(pi+theta)+4cos(pi+theta))/(secc(2pi-theta)-4cot(2pi+theta))= -(5)/(4) '/>

If cos theta=(3)/(5) and theta is not in the first quad-Turito

Solution for the question - if asin theta+b cos,theta=c then (a-b tan theta)/(b+a tan theta)= (+-sqrt(a^(2)+b^(2)+c^(2)))/(b^(2)-c^(2)) '/>(+-sqrt(b^(2)-c^(2)-a^(2)))/(c) '/>

If asin theta+b cos,theta=c then (a-b tan theta)/(b+a tan theta-Turito

<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFQAAAARCAYAAABD/oseAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAg1JREFUeNrtmMFLAkEUxpcOERGBdIiIEEQkQiIIiZDo5iFEROjgISKEDh26e/Bf6BRBSIiH6CLSIbpGSEQQEhHRRSI8dBA6SESIYO/BdxiGcddZZ8FgP/jhzgy+fb557+2slvX/1AMd4o4IW76MaIw4IOp+KMzq1w+BOW0St34YzGgOPTTkh2J4RYgrBNWXgcy8JqZH3dE4+hE3+Q9iR1pPEq84rvBnSmGDy++G+BGON7KyRBP3KRETmr5wMBdd/L4Zogyb/DklrPF422QwV4gWkcZxhEvqXFhfIxpEFOMoxuuSncc+gRbtvBELuM8+caTpS0+Bk8bRb7dwzZt+jLWgzdGrNwBKVYhDG4cqyFA5Yy+lOc7MgI2dKjJU1KemL25UIPLSpjVwzZu1Ybrc2w49qY2dlXe9Lc2lkQnZPna+iVmFbR1f3KgplbiFlpIgTrx6nXOz3lHMseNF9NnIgCWk44uuVomaYj5H3CsCbaTkW4YyVFRe0Zu+iEmHALQMZyg/bC4U82VUkycqDtBDU4ryrjq8a8sZXEJmDOOLrjIKP/kee8hcT/5cCeF4kkEg5okzYT2GJr6E8TLGcRubOTxNRYXxvYTwhC1r+qIrzvZ3tJ8ANvVUOIIVvMpSfvI9EF3iSZGRSRx5OOtekKH9ek4XzqreZGIotS7spFz4oqsgNrcunTd3iWf/XWmE9QeWPpbBnr4NHwAAAI10RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1cD48bWk+Y29zZWM8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPiYjeEEwOzwvbW8+PG1pPiYjeDNCMTs8L21pPjxtbz49PC9tbz48L21hdGg+pz5kywAAAABJRU5ErkJggg==" class="Wirisformula" alt="cosec squared space alpha equals" width="84" height="17" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»cosec«/mi»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mi»§#945;«/mi»«mo»=«/mo»«/math»'/><img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator 4 x y over denominator left parenthesis x plus y right parenthesis squared end fraction left square bracket left parenthesis x comma y right parenthesis" width="103" height="40" style="vertical-align:-17px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»4«/mn»«mi»x«/mi»«mi»y«/mi»«/mrow»«mrow»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«/mrow»«/mfrac»«mo»[«/mo»«mo»(«/mo»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«mo»)«/mo»«/math»'/><img src="data:image/png;base64,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" class="Wirisformula" alt="not equal to left parenthesis 0 comma 0 right parenthesis right square bracket text  is  end text" width="78" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8800;«/mo»«mo»(«/mo»«mn»0«/mn»«mo»,«/mo»«mn»0«/mn»«mo»)«/mo»«mo»]«/mo»«mtext»§#160;is§#160;«/mtext»«/math»'/>possible for x=y. Hence, option(d) is the correct answer.

Solution for the question - cosec^(2)alpha=(4xy)/((x+y)^(2))[(x,y)!=(0,0)] is possible for'/>not possibleimpossible for'/> possible for'/>

Cosec^(2)alpha=(4xy)/((x+y)^(2))[(x,y)!=(0,0)] is -Turito

Solution for the question - if 0 (ji)/(b) '/> (" ji ")/(15) '/> (pi i)/(4) '/> (pi)/(6) '/>

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AB is a line segment of length 24 cm and C is its middle point. On AB, A and CB semi-circles are described. The radius of circle which touches all these semi-circles is

$3 c m$
$6 c m$
$4 c m$
$8 c m$

The correct answer is: $8 text end text c m$

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in a $triangle P Q R$ $3 sin space P plus 4 cos space Q equals 6$ and $4 sin space Q plus 3 cos$ p=1 then

The expression $fraction numerator tan space A over denominator 1 minus cat space A end fraction plus fraction numerator cot space A over denominator 1 minus tan space d end fraction$ can be written as

The expression $fraction numerator tan space A over denominator 1 minus cat space A end fraction plus fraction numerator cot space A over denominator 1 minus tan space d end fraction$ can be written as

Two arcs of same length of two different circles subtended angles of $25 to the power of ring operator$ and $75 to the power of ring operator$ at their centers respectively. Then the ratio of the radii of the circles is

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$straight a equals sec space 2 to the power of ring operator comma straight b equals sec space 2 rightwards double arrow$

$straight a equals sec space 2 to the power of ring operator comma straight b equals sec space 2 rightwards double arrow$

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I $x equals cos invisible function application 1 to the power of ring operator comma y equals cos invisible function application 1 not stretchy rightwards double arrow$

If ABCD is a cynic quadrilateral such that 12 tan $A minus 5 equals 0$ and 5cos B+3=0, then cos C tan D=

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$integral fraction numerator d x over denominator square root of x squared plus 2 x plus 1 end root end fraction$ = A log |x + 1| + C for x < – 1 then A is -

$integral fraction numerator d x over denominator square root of x squared plus 2 x plus 1 end root end fraction$ = A log |x + 1| + C for x < – 1 then A is -

$cos space A comma sin space A comma cot space A space$ are in then $tan to the power of 6 straight A minus tan squared space of 1em straight A equals$

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$text If end text a sin space theta plus b cos comma theta equals c text then end text fraction numerator a minus b tan space theta over denominator b plus a tan space theta end fraction equals$

$text If end text a sin space theta plus b cos comma theta equals c text then end text fraction numerator a minus b tan space theta over denominator b plus a tan space theta end fraction equals$

$text If end text 0 less or equal than x less or equal than pi comma 81 to the power of sin squared space x end exponent plus 81 to the power of cos squared space x end exponent equals 30 text then end text x equals$

$text If end text 0 less or equal than x less or equal than pi comma 81 to the power of sin squared space x end exponent plus 81 to the power of cos squared space x end exponent equals 30 text then end text x equals$

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AB is a line segment of length 24 cm and C is its middle point. On AB, A and CB semi-circles are described. The radius of circle which touches all these semi-circles is

The correct answer is:

Related Questions to study

in a and p=1 then

in a and p=1 then

The expression can be written as

The expression can be written as

if where then

if where then

Two arcs of same length of two different circles subtended angles of and at their centers respectively. Then the ratio of the radii of the circles is

Two arcs of same length of two different circles subtended angles of and at their centers respectively. Then the ratio of the radii of the circles is

Let and then

Let and then

I

I

If ABCD is a cynic quadrilateral such that 12 tan and 5cos B+3=0, then cos C tan D=

If ABCD is a cynic quadrilateral such that 12 tan and 5cos B+3=0, then cos C tan D=

= A log |x + 1| + C for x < – 1 then A is -

= A log |x + 1| + C for x < – 1 then A is -

are in then

are in then

If cos and is not in the first quadrant, then

If cos and is not in the first quadrant, then

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The correct answer is: $8 text end text c m$

in a $triangle P Q R$ $3 sin space P plus 4 cos space Q equals 6$ and $4 sin space Q plus 3 cos$ p=1 then

in a $triangle P Q R$ $3 sin space P plus 4 cos space Q equals 6$ and $4 sin space Q plus 3 cos$ p=1 then

The expression $fraction numerator tan space A over denominator 1 minus cat space A end fraction plus fraction numerator cot space A over denominator 1 minus tan space d end fraction$ can be written as

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Two arcs of same length of two different circles subtended angles of $25 to the power of ring operator$ and $75 to the power of ring operator$ at their centers respectively. Then the ratio of the radii of the circles is

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I $x equals cos invisible function application 1 to the power of ring operator comma y equals cos invisible function application 1 not stretchy rightwards double arrow$

I $x equals cos invisible function application 1 to the power of ring operator comma y equals cos invisible function application 1 not stretchy rightwards double arrow$

If ABCD is a cynic quadrilateral such that 12 tan $A minus 5 equals 0$ and 5cos B+3=0, then cos C tan D=

If ABCD is a cynic quadrilateral such that 12 tan $A minus 5 equals 0$ and 5cos B+3=0, then cos C tan D=

$integral fraction numerator d x over denominator square root of x squared plus 2 x plus 1 end root end fraction$ = A log |x + 1| + C for x < – 1 then A is -

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