tan frac{pi}{5}+2 tan frac{2 pi}{5}+4 cot fra | vedclass

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Question

(A) We use the identity $2 \cot 2A + 	an A = \cot A$ ... $(i)$.Given expression: $E = 	an \frac{\pi}{5} + 2 	an \frac{2 \pi}{5} + 4 \cot \frac{4 \p

Vedclass · Accepted Answer

$\cot \frac{\pi}{5}$

Vedclass · Answer

(A) We use the identity $2 \cot 2A + 	an A = \cot A$ ... $(i)$.Given expression: $E = 	an \frac{\pi}{5} + 2 	an \frac{2 \pi}{5} + 4 \cot \frac{4 \pi}{5}$.$E = 	an \frac{\pi}{5} + 2 \left[ 	an \frac{2 \pi}{5} + 2 \cot \frac{4 \pi}{5} ight]$.Using identity $(i)$ with $A = \frac{2 \pi}{5}$,we have $	an \frac{2 \pi}{5} + 2 \cot \frac{4 \pi}{5} = \cot \frac{2 \pi}{5}$.So,$E = 	an \frac{\pi}{5} + 2 \cot \frac{2 \pi}{5}$.Using identity $(i)$ with $A = \frac{\pi}{5}$,we have $	an \frac{\pi}{5} + 2 \cot \frac{2 \pi}{5} = \cot \frac{\pi}{5}$.Therefore,the value is $\cot \frac{\pi}{5}$.

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

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