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AP EAMCET · Maths · Trigonometric Ratios & Identities

\(\tan \frac{\pi}{5}+2 \tan \frac{2 \pi}{5}+4 \cot \frac{4 \pi}{5}\) is equal to

  1. A \(\cot \frac{\pi}{5}\)
  2. B \(\cot \frac{2\pi}{5}\)
  3. C \(\cot \frac{3\pi}{5}\)
  4. D \(\cot \frac{4\pi}{5}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\cot \frac{\pi}{5}\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \text { (a) Given, } \tan \frac{\pi}{5}+2 \tan \frac{2 \pi}{5}+4 \cot \frac{4 \pi}{5} \\ & =\tan \frac{\pi}{5}+2\left[2 \cot \frac{4 \pi}{5}+\tan \frac{2 \pi}{5}\right] \end{aligned}\) We know that, \(2 \cot 2 A+\tan A=\cot A\) ...(i)…