The value of cos left(frac{2 pi}{7}right)+cos | vedclass

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Question

$\cos \frac{2 \pi}{7}+\cos \frac{4 \pi}{7}+\cos \frac{6 \pi}{7}$

$=\frac{\sin \left(3 	imes \frac{\pi}{7}ight)}{\sin \frac{\pi}{7}} 	imes \cos

Vedclass · Accepted Answer

$-\frac{1}{2}$

Vedclass · Answer

$\cos \frac{2 \pi}{7}+\cos \frac{4 \pi}{7}+\cos \frac{6 \pi}{7}$

$=\frac{\sin \left(3 	imes \frac{\pi}{7}ight)}{\sin \frac{\pi}{7}} 	imes \cos \left(\frac{\frac{2 \pi}{7}+\frac{6 \pi}{7}}{2}ight)$

$=\frac{2 \sin \left(\frac{3 \pi}{7}ight)}{2 \sin \frac{\pi}{7}} 	imes \cos \left(\frac{4 \pi}{7}ight)$

$=\frac{\sin \left(\frac{7 \pi}{7}ight)+\sin \left(\frac{-\pi}{7}ight)}{2 \sin \frac{\pi}{7}}$

$=\frac{-\sin \frac{\pi}{7}}{2 \sin \frac{\pi}{7}}$

$=-\frac{1}{2}$

The value of $\cos \left(\frac{2 \pi}{7}\right)+\cos \left(\frac{4 \pi}{7}\right)+\cos \left(\frac{6 \pi}{7}\right)$ is equal to

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