QJEEM22Maea15: JEE Main 2022 Mathematics - Class 11 JEEM22Maea15 Solution

$2\sin {\pi \over {22}}\sin {{3\pi } \over {22}}\sin {{5\pi } \over {22}}\sin {{7\pi } \over {22}}\sin {{9\pi } \over {22}}$

$= 2\sin \left( {{{11\pi - 10\pi } \over {22}}} \right)\sin \left( {{{11\pi - 8\pi } \over {22}}} \right)\sin \left( {{{11\pi - 6\pi } \over {22}}} \right)\sin \left( {{{11\pi - 4\pi } \over {22}}} \right)\sin \left( {{{11\pi - 2\pi } \over {22}}} \right)$

$= 2\cos {\pi \over {11}}\cos {{2\pi } \over {11}}\cos {{3\pi } \over {11}}\cos {{4\pi } \over {11}}\cos {{5\pi } \over {11}}$

$= {{2\sin {{32\pi } \over {11}}} \over {{2^5}\sin {\pi \over {11}}}}$

$= {1 \over {16}}$