2 15 4 15 8 15 16 15 = - Vidyadip

MCQ

$\cos \frac{{2\pi }}{{15}}\cos \frac{{4\pi }}{{15}}\cos \frac{{8\pi }}{{15}}\cos \frac{{16\pi }}{{15}} =$

A
$1/2$
B
$1/4$
C
$1/8$
✓
$1/16$

✓

Answer

Correct option: D.

$1/16$

d
(d) $\cos \frac{{2\pi }}{{15}}\cos \frac{{4\pi }}{{15}}\cos \frac{{8\pi }}{{15}}\cos \frac{{16\pi }}{{15}}$

$ = \frac{{\sin \,{2^4}\frac{{2\pi }}{{15}}}}{{{2^4}\sin \frac{{2\pi }}{{15}}}} $

$= \frac{{\sin \,\frac{{32\pi }}{{15}}}}{{16\,\sin \frac{{2\pi }}{{15}}}} $

$= \frac{1}{{16}}\frac{{\sin \frac{{2\pi }}{{15}}}}{{\sin \frac{{2\pi }}{{15}}}} $

$= \frac{1}{{16}}$.

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