Cos frac{{2π }}{{15}}cos frac{{4π }}{{15}}cos frac{{8π }}{{15}}cos frac{{16π }}{{15}} =

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3.Trigonometrical Ratios, Functions and Identities

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

$1/2$

$1/4$

$1/8$

$1/16$

(IIT-1985)

(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}}}} $

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

Standard 11

Mathematics

easy

normal

medium

medium

easy