AP EAMCET · Maths · Trigonometric Ratios & Identities
\(\tan \alpha+2 \tan 2 \alpha+4 \tan 4 \alpha+8 \cot 8 \alpha=\)
- A \(\sin \alpha\)
- B \(\cos \alpha\)
- C \(\tan \alpha\)
- D \(\cot \alpha\)
Answer & Solution
Correct Answer
(D) \(\cot \alpha\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { As, } \tan \theta-\cot \theta=\frac{\sin ^2 \theta-\cos ^2 \theta}{\sin \theta \cos \theta}=-2 \cot 2 \theta \\ & \text { Now, } \tan \alpha+2 \tan 2 \alpha+4 \tan 4 \alpha+8 \cot 8 \alpha \\ & =\tan \alpha-\cot \alpha+2 \tan 2 \alpha+4 \tan 4 \alpha+8…
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