The value of tan frac{pi}{3} + 2 tan frac{2 p | vedclass

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(A) We know that $	an \frac{\pi}{3} = \sqrt{3}$.$	an \frac{2 \pi}{3} = 	an(\pi - \frac{\pi}{3}) = -	an \frac{\pi}{3} = -\sqrt{3}$.$	an \frac{4 \p

Vedclass · Accepted Answer

$-5$

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(A) We know that $	an \frac{\pi}{3} = \sqrt{3}$.$	an \frac{2 \pi}{3} = 	an(\pi - \frac{\pi}{3}) = -	an \frac{\pi}{3} = -\sqrt{3}$.$	an \frac{4 \pi}{3} = 	an(\pi + \frac{\pi}{3}) = 	an \frac{\pi}{3} = \sqrt{3}$.$	an \frac{8 \pi}{3} = 	an(2 \pi + \frac{2 \pi}{3}) = 	an \frac{2 \pi}{3} = -\sqrt{3}$.Substituting these values into the expression:$\sqrt{3} + 2(-\sqrt{3}) + 4(\sqrt{3}) + 8(-\sqrt{3})$$= \sqrt{3} - 2 \sqrt{3} + 4 \sqrt{3} - 8 \sqrt{3}$$= (1 - 2 + 4 - 8) \sqrt{3}$$= -5 \sqrt{3}$.

The value of $\tan \frac{\pi}{3} + 2 \tan \frac{2 \pi}{3} + 4 \tan \frac{4 \pi}{3} + 8 \tan \frac{8 \pi}{3}$ is equal to (in $\sqrt{3}$)

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