The value of cos ,frac{pi }{7},cos ,frac{{2pi | vedclass

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Question

$\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{3 \pi}{7}$

$=\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \left(\pi-\frac{4 \pi}{7}\right)$

Vedclass · Accepted Answer

$1/8$

Vedclass · Answer

$\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{3 \pi}{7}$

$=\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \left(\pi-\frac{4 \pi}{7}\right)$

$=-\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7}$

$=-\left[\frac{\sin \left(2^{3} \cdot \frac{\pi}{7}\right)}{2^{3} \sin \frac{\pi}{7}}\right]$

$=-\frac{\sin \frac{8 \pi}{7}}{8 \sin \frac{\pi}{7}}=\frac{1}{8}$

The value of $\cos \,\frac{\pi }{7}\,\cos \,\frac{{2\pi }}{7}\,\cos \,\frac{{3\pi }}{7}$ is

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