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Question

$text If end text c o s to the power of 2 end exponent invisible function application x plus c o s to the power of 4 end exponent invisible function application x equals 1 text , then the value of end text t a n to the power of 4 end exponent invisible function application x plus c o t to the power of 4 end exponent invisible function application x plus t a n to the power of 2 end exponent invisible function application x minus c o t to the power of 2 end exponent invisible function application x text is equal to end text$

0
2
1
None of these

The correct answer is: 2

Given $blank c o s to the power of 2 end exponent invisible function application x plus c o s to the power of 4 end exponent invisible function application x equals 1$
$c o s to the power of 4 end exponent invisible function application x equals s i n to the power of 2 end exponent invisible function application x rightwards double arrow c o t to the power of 4 end exponent invisible function application x equals c o s e c to the power of 2 end exponent invisible function application x$
$table row cell text end text text N end text text o end text text w end text text , end text text end text end cell row cell t a n to the power of 4 end exponent invisible function application x plus c o t to the power of 4 end exponent invisible function application x plus t a n to the power of 2 end exponent invisible function application x minus c o t to the power of 2 end exponent invisible function application x end cell end table$
$equals t a n to the power of 2 end exponent invisible function application x open parentheses 1 plus t a n to the power of 2 end exponent invisible function application x close parentheses plus c o s e c to the power of 2 end exponent invisible function application x minus c o t to the power of 2 end exponent invisible function application x$
$equals t a n to the power of 2 end exponent invisible function application x times s e c to the power of 2 end exponent invisible function application x plus 1$
$equals fraction numerator sin to the power of 2 end exponent invisible function application x over denominator cos to the power of 4 end exponent invisible function application x end fraction plus 1 equals 2$

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If cot $theta equals fraction numerator square root of m plus square root of n over denominator square root of m minus square root of n end root end fraction$ ,then $left parenthesis m plus n right parenthesis$ cos $2 theta$ is equal to

On bombarding $U to the power of 235 end exponent$ by slow neutrons, 200MeV energy is released. If the power output of atomic reactor is 1.6 MW, then the rate of fission will be

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if cos $left parenthesis x minus y right parenthesis$ , cos x and cos $left parenthesis x plus y right parenthesis$ are in HP, then cos $x times s e c invisible function application fraction numerator y over denominator 2 end fraction$ is equal to

if cos $left parenthesis x minus y right parenthesis$ , cos x and cos $left parenthesis x plus y right parenthesis$ are in HP, then cos $x times s e c invisible function application fraction numerator y over denominator 2 end fraction$ is equal to

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if cot $alpha c o t invisible function application beta equals 2$ , then $fraction numerator c o s invisible function application left parenthesis alpha plus beta right parenthesis over denominator c o s invisible function application left parenthesis alpha minus beta right parenthesis end fraction$ is equal to

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Given $blank fraction numerator pi over denominator 2 end fraction less than alpha less than pi$ ,then the expression $square root of fraction numerator 1 minus s i n invisible function application alpha over denominator 1 plus s i n invisible function application alpha end fraction end root plus square root of fraction numerator 1 plus s i n invisible function application alpha over denominator 1 minus s i n invisible function application alpha end fraction end root$ s equal to $blank$

Given $blank fraction numerator pi over denominator 2 end fraction less than alpha less than pi$ ,then the expression $square root of fraction numerator 1 minus s i n invisible function application alpha over denominator 1 plus s i n invisible function application alpha end fraction end root plus square root of fraction numerator 1 plus s i n invisible function application alpha over denominator 1 minus s i n invisible function application alpha end fraction end root$ s equal to $blank$

$text Find the value of end text x text if end text x equals fraction numerator 1 minus 4 s i n invisible function application 10 to the power of ring operator end exponent s i n invisible function application 70 to the power of ring operator end exponent over denominator 2 s i n invisible function application 10 to the power of ring operator end exponent end fraction text . end text$

$text Find the value of end text x text if end text x equals fraction numerator 1 minus 4 s i n invisible function application 10 to the power of ring operator end exponent s i n invisible function application 70 to the power of ring operator end exponent over denominator 2 s i n invisible function application 10 to the power of ring operator end exponent end fraction text . end text$

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$text If end text x comma y comma z text are in AP, then end text fraction numerator s i n invisible function application x minus s i n invisible function application z over denominator c o s invisible function application z minus c o s invisible function application x end fraction text is equal to end text$

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$s i n invisible function application fraction numerator pi over denominator 9 end fraction s i n invisible function application fraction numerator 2 pi over denominator 9 end fraction s i n invisible function application fraction numerator 4 pi over denominator 9 end fraction s i n invisible function application fraction numerator pi over denominator 3 end fraction text is equal to end text$

$s i n invisible function application fraction numerator pi over denominator 9 end fraction s i n invisible function application fraction numerator 2 pi over denominator 9 end fraction s i n invisible function application fraction numerator 4 pi over denominator 9 end fraction s i n invisible function application fraction numerator pi over denominator 3 end fraction text is equal to end text$

parallel

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