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Maths-

General

Easy

Question

If $tan space theta plus tan space open parentheses theta plus pi over 3 close parentheses plus tan space open parentheses theta plus fraction numerator 2 pi over denominator 3 end fraction close parentheses equals 3$ then which of the following is equal to 1

$\tan 2 θ$
$\tan 3 θ$
$t a n^{2} θ$
$t a n^{3} θ$

The correct answer is: $tan space 3 theta$

sol. $tan space theta plus tan space open parentheses theta plus 60 to the power of ring operator close parentheses plus tan space open parentheses theta plus 120 to the power of ring operator close parentheses equals 3 tan space 3 theta$

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$sin space 12 to the power of ring operator sin space 48 to the power of ring operator sin space 54 to the power of ring operator equals$

$sin space 12 to the power of ring operator sin space 48 to the power of ring operator sin space 54 to the power of ring operator equals$

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$cos to the power of 6 space A plus sin to the power of 6 space A equals 1 minus k sin squared space left parenthesis 2 A right parenthesis not stretchy rightwards double arrow k equals$

If $180 to the power of ring operator less than theta less than 270 to the power of 0 comma c o t space theta equals 4 divided by 3$

If $180 to the power of ring operator less than theta less than 270 to the power of 0 comma c o t space theta equals 4 divided by 3$

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$tan space A equals fraction numerator 1 minus cos space B over denominator sin begin display style space end style B end fraction not stretchy rightwards double arrow tan space 2 A minus tan space B equals$

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$4 cos cubed space 40 to the power of ring operator minus 3 sin space 50 to the power of ring operator equals$

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parallel

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$fraction numerator sin space 12 A over denominator sin space 4 A end fraction minus fraction numerator cos begin display style space end style 12 A over denominator cos begin display style space end style 4 A end fraction equals$

If $tan space alpha equals square root of a comma$ where a is rational number which is not a perfect square, then which of the following is a rational number.

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$cot space theta equals fraction numerator 2 tan space 71 divided by 2 to the power of ring operator 0 over denominator 1 minus tan squared space 71 divided by 2 end fraction$ then $sin space 3 theta equals$

$cot space theta equals fraction numerator 2 tan space 71 divided by 2 to the power of ring operator 0 over denominator 1 minus tan squared space 71 divided by 2 end fraction$ then $sin space 3 theta equals$

parallel

$fraction numerator sin space theta plus sin space 2 theta over denominator 1 plus cos space theta plus cos space 2 theta end fraction equals$

$fraction numerator sin space theta plus sin space 2 theta over denominator 1 plus cos space theta plus cos space 2 theta end fraction equals$

If $s i n squared space A equals x$ , then $sin space A sin space 2 A sin space 3 A sin space 4 A$ is a polynomial in $x$ , the sum of whose coefficients is

If $s i n squared space A equals x$ , then $sin space A sin space 2 A sin space 3 A sin space 4 A$ is a polynomial in $x$ , the sum of whose coefficients is

The range of all values of $theta to the power of blank$ such that $sin space 3 theta minus cos space 3 theta greater than 0$

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A me tall ic rod e cm long, A squar e cm h cross-section is heated through t" C. If Young's modulus of elasticity of the metal is E and the mean c oeffic ient of linear expansion is a per degree celsius, then the compressional force required to prevent the rod from expanding along it s length is

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