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

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Question

(A) We know that $	an 	heta + 2 	an 2 	heta + 4 \cot 4 	heta = \cot 	heta$. Let $	heta = \frac{\pi}{5} = 36^{\circ}$. Then the expression becom

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) We know that $	an 	heta + 2 	an 2 	heta + 4 \cot 4 	heta = \cot 	heta$. Let $	heta = \frac{\pi}{5} = 36^{\circ}$. Then the expression becomes $	an \frac{\pi}{5} + 2 	an \frac{2 \pi}{5} + 4 \cot \frac{4 \pi}{5}$. Using the identity $	an 	heta + 2 	an 2 	heta + 4 	an 4 	heta + 8 \cot 8 	heta = \cot 	heta$ is not directly applicable,but we can use the identity $	an 	heta + 2 	an 2 	heta + 4 \cot 4 	heta = \cot 	heta$. Substituting $	heta = \frac{\pi}{5}$,we get $	an \frac{\pi}{5} + 2 	an \frac{2 \pi}{5} + 4 \cot \frac{4 \pi}{5} = \cot \frac{\pi}{5}$. Thus,the correct option is $A$.

$\tan \frac{\pi}{5} + 2 \tan \frac{2 \pi}{5} + 4 \cot \frac{4 \pi}{5} = $

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