Cos frac{π }{7}cos frac{{2π }}{7}cos frac{{4π }}{7} =

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3.Trigonometrical Ratios, Functions and Identities

easy

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

A

$0$

B

$\frac{1}{2}$

C

$\frac{1}{4}$

D

$ - \frac{1}{8}$

Solution

(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] $

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

$= – \frac{1}{8}$.

Standard 11

Mathematics

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