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Question: Answered & Verified by Expert
If $A$ is not an integral multiple of $\frac{\pi}{2}$, then $\operatorname{cosec} 2 A+\cot 2 A$ is equal to
MathematicsTrigonometric Ratios & IdentitiesTS EAMCETTS EAMCET 2021 (06 Aug Shift 2)
Options:
  • A tan A
  • B $\cot A+2 \cot 2 A$
  • C $\tan A+2 \cot 2 A$
  • D tan2 A
Solution:
1899 Upvotes Verified Answer
The correct answer is: $\tan A+2 \cot 2 A$
$\begin{aligned} & \operatorname{cosec} 2 A+\cot 2 A=\frac{1+\cos 2 A}{\sin 2 A} \\ & =\frac{1+2 \cos ^2 A-1}{\sin 2 A}=\cot A \\ & =\frac{1}{\tan A}=\frac{\tan ^2 A+1-\tan ^2 A}{\tan A} \\ & =\tan A+\frac{1-\tan ^2 A}{\tan A} \\ & =\tan A+\frac{2\left(1-\tan ^2 A\right)}{2 \tan A}=\tan A+2 \frac{1}{\tan 2 A} \\ & =\tan A+2 \cot 2 A\end{aligned}$

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