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Questions  >>  CBSE XI  >>  Math  >>  Trigonometric Functions
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Q)

Evaluate : $\cot ^4\theta+\cot ^2\theta$

$\begin{array}{1 1}(A)\;1&(B)\;cosec^4\theta-cosec^2\theta\\(C)\;cosec^4\theta+cosec^2\theta&(D)\;\text{None of these}\end{array} $

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A)
Toolbox:
  • $\cot \theta=\pm \sqrt{cosec^2\theta-1}$
  • $cosec^2\theta-1=\cot^2\theta$
  • $(a-b)^2=a^2+b^2-2ab$
$\cot ^4\theta+\cot ^2\theta$
$\Rightarrow (\cot^2\theta)^2+\cot^2\theta$
$\Rightarrow (cosec^2\theta-1)^2+(cosec^2\theta-1)$
$\Rightarrow cosec^4\theta+1-2cosec^2\theta+cosec^2\theta-1$
$\Rightarrow cosec^4\theta-cosec^2\theta$
Hence (B) is the correct answer.
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