JEE MATHEMATICS MCQ: MULTIPLE AND SUBMULTIPLE ANGLES

1 Easy

1 of 1

Application +4 | -1

The value of

\cos \,\,\frac{\pi }{{15}}\,\,\cos \,\,\frac{{2\,\pi }}{{15}}\,\,\cos \,\,\frac{{3\,\pi }}{{15}}\,\,\cos \,\,\frac{{4\,\pi }}{{15}}\,\,\cos \,\,\frac{{5\,\pi }}{{15}}\,\,\cos \,\,\frac{{6\,\pi }}{{15}}\,\,\cos \,\,\frac{{7\pi }}{{15}}

, is

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Correct option: A

1/128

Option A (

1/128

) is correct because the expression can be simplified using the identity

\prod_{k=1}^{n-1} \cos(\frac{k\pi}{2n}) = \frac{\sqrt{n}}{2^{n-1}}

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