The value of ${\rm{\;}}\cos \,\,\frac{{\rm{\pi }}}{5}\,\,\cos \,\,\frac{{2\,{\rm{\pi }}}}{5}\,\,\cos \,\,\frac{{4\,{\rm{\pi }}}}{5}\,\,\cos \,\,\frac{{8\,{\rm{\pi }}}}{5}{\rm{\;}}$ is equal to

JEE MATHEMATICS MCQ: TRANSFORMATIONS

1 Easy

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The value of

\mathrm{\;}\cos \,\,\frac{\mathrm{\pi }}{5}\,\,\cos \,\,\frac{{2\,\mathrm{\pi }}}{5}\,\,\cos \,\,\frac{{4\,\mathrm{\pi }}}{5}\,\,\cos \,\,\frac{{8\,\mathrm{\pi }}}{5}\mathrm{\;}

is equal to

View answer and explanation

Correct option: D

- \frac{1}{{16}}

Option D (

- \frac{1}{{16}}

) is correct because it is the result of applying the product-to-sine identity repeatedly and simplifying.

Practice All Chapter MCQs →

1 + \cos \,\,56^\circ + \cos \,\,58^\circ - \cos \,\,66^\circ = \lambda \cos \,\,28^\circ \,\,\cos \,\,29^\circ \,\,\sin \,\,33^\circ

\lambda =

\cos \,\,\frac{\pi }{{11}} + \cos \,\,\frac{{3\,\pi }}{{11}} + \cos \,\,\frac{{5\,\pi }}{{11}} + \cos \,\,\frac{{7\pi }}{{11}} + \cos \,\,\frac{{9\,\pi }}{{11}}

\;\cos \,\,x + \cos \,\,y + \cos \,\,\alpha = 0\;\,\mathrm{and}\,\sin x + \sin \,\,y + \sin \,\,\alpha = 0

\cot \left( {\frac{{x + y}}{2}} \right)\;

f\left( x \right) = \sin \left( {\frac{{2x + 3}}{{6\;\pi }}} \right),

0 < x,\mathrm{ }y < \pi

\cos x + \cos y - \cos (x + y) = \frac{3}{2}

\sin x + \cos y

\mathrm{\;sin}\,\,36^\circ \,\,\sin \,\,72^\circ \,\,\sin \,\,108^\circ \,\,\sin \,\,144^\circ \;