7 2 7 3 7 = - Vidyadip

MCQ

$\cos \frac{\pi }{7}\cos \frac{{2\pi }}{7}\cos \frac{{3\pi }}{7} =$

A
$-\frac{1}{8}$
B
$\frac{1}{16}$
✓
$\frac{1}{8}$
D
None

✓

Answer

Correct option: C.

$\frac{1}{8}$

c
$\frac{1}{2 \sin \frac{\pi}{7}}\left[2 \sin \frac{\pi}{7} \cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{\pi}{7}\right]$

$\frac{1}{2 \times 2 \sin \frac{\pi}{7}}\left[2 \sin \frac{2 \pi}{7} \cos \frac{2 \pi}{7} \cos \frac{3 \pi}{7}\right]$

$\frac{1}{2.4\sin \left(\frac{\pi}{3}\right)}\left(2 \sin 4 \frac{\pi}{7} \cos \frac{3 \pi}{7}\right)$

$\frac{1}{8 \sin \left(\frac{\pi}{7}\right)}\left[\sin (\pi)+\sin \left(\frac{\pi}{7}\right)\right]$

$\frac{\sin (\pi / 7)}{8 \sin (\pi / 7)}=\frac{1}{8}$

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