cos frac{{2pi }}{{15}}cos frac{{4pi }}{{15}}c | vedclass

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Question

(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 }}{{

Vedclass · Accepted Answer

$1/16$

Vedclass · Answer

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

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

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