5 2 5 4 5 8 5 = - Vidyadip

MCQ

$\cos \frac{\pi }{5}\cos \frac{{2\pi }}{5}\cos \frac{{4\pi }}{5}\cos \frac{{8\pi }}{5} = $

A
$1/16$
B
$0$
C
$-1/8$
✓
$-1/16$

✓

Answer

Correct option: D.

$-1/16$

d
(d) $\cos \frac{\pi }{5}\cos \frac{{2\pi }}{5}\cos \frac{{4\pi }}{5}\cos \frac{{8\pi }}{5}$

$ = \frac{{\sin \frac{{{2^4}\pi }}{5}}}{{{2^4}\sin \frac{\pi }{5}}} = \frac{{\sin \frac{{16\pi }}{5}}}{{16\,\sin \frac{\pi }{5}}} $

$= \frac{{\sin \,\left( {3\pi + \frac{\pi }{5}} \right)}}{{16\,\sin \frac{\pi }{5}}}$

$ = \frac{{ - \sin \frac{\pi }{5}}}{{16\,\sin \frac{\pi }{5}}} = - \frac{1}{{16}}$.

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