TS EAMCET · Maths · Trigonometric Ratios & Identities
If \(A\) is not an integral multiple of \(\frac{\pi}{2}\), then \(\operatorname{cosec} 2 A+\cot 2 A\) is equal to
- A tan A
- B \(\cot A+2 \cot 2 A\)
- C \(\tan A+2 \cot 2 A\)
- D tan2 A
Answer & Solution
Correct Answer
(C) \(\tan A+2 \cot 2 A\)
Step-by-step Solution
Detailed explanation
\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…
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