$I f A i s n o t a n i n t e g r a l m u l t i p l e o f \frac{π}{2}, t h e n \cos e c 2 A + c o t 2 A =$

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cot A + 2cot 2A

tan A + 2cot 2A

tan 2A

tan A

answer is C.

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Detailed Solution

$\begin{array}{rcl} cosec 2 A + \cot 2 A \\ = & \frac{1 + \tan^{2} A}{2 \tan A} + \frac{1 - \tan^{2} A}{2 \tan A} \\ = & \frac{1 + \tan^{2} A + 1 - \tan^{2} A}{2 \tan A} \\ = & \frac{2}{2 \tan A} = \cot A \end{array}$

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