The value of ${\rm{\;\;}}\left( {1 + {\rm{cos}}\,\,\frac{{\rm{\pi }}}{8}} \right)\,\,\left( {1 + {\rm{cos}}\,\,\frac{{3{\rm{\pi }}}}{8}} \right)\,\,\left( {1 + {\rm{cos}}\,\,\frac{{5{\rm{\pi }}}}{8}} \right)\,\,\left( {1 + {\rm{cos}}\,\,\frac{{7{\rm{\pi }}}}{8}} \right){\rm{\;}}$ is equal to

JEE MATHEMATICS MCQ: MULTIPLE AND SUBMULTIPLE ANGLES

1 Easy

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The value of

\mathrm{\;\;}\left( {1 + \mathrm{cos}\,\,\frac{\mathrm{\pi }}{8}} \right)\,\,\left( {1 + \mathrm{cos}\,\,\frac{{3\mathrm{\pi }}}{8}} \right)\,\,\left( {1 + \mathrm{cos}\,\,\frac{{5\mathrm{\pi }}}{8}} \right)\,\,\left( {1 + \mathrm{cos}\,\,\frac{{7\mathrm{\pi }}}{8}} \right)\mathrm{\;}

is equal to

View answer and explanation

Correct option: C

\frac{1}{8}

Option D (

n\pi \\ + \\ \frac{\pi }{4}

) is correct because by simplifying the equation, we get

\tan \theta = 1

, which gives the general solution

\theta = n\pi + \frac{\pi}{4}