The value of ${\rm{\;}}\cos \,\,\frac{{\rm{\pi }}}{{65}}\,\,\cos \,\,\frac{{2\,{\rm{\pi }}}}{{65}}\,\,{\rm{cos}}\,\,\frac{{4\,{\rm{\pi }}}}{{65}}\,\, \ldots \,\,\cos \,\,\frac{{32\,{\rm{\pi }}}}{{65}}$ is

JEE MATHEMATICS MCQ: MULTIPLE AND SUBMULTIPLE ANGLES

1 Easy

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The value of

\mathrm{\;}\cos \,\,\frac{\mathrm{\pi }}{{65}}\,\,\cos \,\,\frac{{2\,\mathrm{\pi }}}{{65}}\,\,\mathrm{cos}\,\,\frac{{4\,\mathrm{\pi }}}{{65}}\,\, \ldots \,\,\cos \,\,\frac{{32\,\mathrm{\pi }}}{{65}}

View answer and explanation

Correct option: B

\frac{1}{{64}}

Option B (

\frac{1}{{64}}

) is correct because repeated application of the identity

\sin 2x = 2 \sin x \cos x

simplifies the expression.