7 2 7 4 7 = - Vidyadip

MCQ

$\cos \frac{\pi }{7}\cos \frac{{2\pi }}{7}\cos \frac{{4\pi }}{7} = $

A
$0$
B
$\frac{1}{2}$
C
$\frac{1}{4}$
✓
$ - \frac{1}{8}$

✓

Answer

Correct option: D.

$ - \frac{1}{8}$

d
(d) $\cos \frac{\pi }{7}.\cos \frac{{2\pi }}{7}.\cos \frac{{4\pi }}{7} $

$= \left[ {\frac{{\sin \left( {{2^3}.\frac{\pi }{7}} \right)}}{{{2^3}\sin \left( {\frac{\pi }{7}} \right)}}} \right] $

$= \frac{{\sin \frac{{8\pi }}{7}}}{{8\sin \frac{\pi }{7}}}$

$= - \frac{1}{8}$.

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