sin frac{2 pi}{5}+sin frac{4 pi}{5}+sin frac{ | vedclass

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(A) We are given the expression: $S = \sin \frac{2 \pi}{5}+\sin \frac{4 \pi}{5}+\sin \frac{6 \pi}{5}+\sin \frac{8 \pi}{5}$ Using the property $\sin(2\

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(A) We are given the expression: $S = \sin \frac{2 \pi}{5}+\sin \frac{4 \pi}{5}+\sin \frac{6 \pi}{5}+\sin \frac{8 \pi}{5}$ Using the property $\sin(2\pi - 	heta) = -\sin 	heta$: $\sin \frac{8 \pi}{5} = \sin(2\pi - \frac{2 \pi}{5}) = -\sin \frac{2 \pi}{5}$ $\sin \frac{6 \pi}{5} = \sin(2\pi - \frac{4 \pi}{5}) = -\sin \frac{4 \pi}{5}$ Substituting these into the expression: $S = \sin \frac{2 \pi}{5} + \sin \frac{4 \pi}{5} - \sin \frac{4 \pi}{5} - \sin \frac{2 \pi}{5}$ $S = 0$

$\sin \frac{2 \pi}{5}+\sin \frac{4 \pi}{5}+\sin \frac{6 \pi}{5}+\sin \frac{8 \pi}{5}$ is equal to

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