QJEEM21Maa24b: JEE Main 2021 Mathematics - Class 11 JEEM21Maa24b Solution

Question

Verified Solution • 2025–26 Session moderate

The value of

2\sin \left( {{\pi \over 8}} \right)\sin \left( {{{2\pi } \over 8}} \right)\sin \left( {{{3\pi } \over 8}} \right)\sin \left( {{{5\pi } \over 8}} \right)\sin \left( {{{6\pi } \over 8}} \right)\sin \left( {{{7\pi } \over 8}} \right)

is :

Accepted Answer

2\sin \left( {{\pi \over 8}} \right)\sin \left( {{{2\pi } \over 8}} \right)\sin \left( {{{3\pi } \over 8}} \right)\sin \left( {{{5\pi } \over 8}} \right)\sin \left( {{{6\pi } \over 8}} \right)\sin \left( {{{7\pi } \over 8}} \right)

2{\sin ^2}{\pi \over 8}{\sin ^2}{{2\pi } \over 8}{\sin ^2}{{3\pi } \over 8}

{\sin ^2}{\pi \over 8}{\sin ^2}{{3\pi } \over 8}

{\sin ^2}{\pi \over 8}{\cos ^2}{\pi \over 8}

{1 \over 4}{\sin ^2}\left( {{\pi \over 4}} \right) = {1 \over 8}

Step-by-Step Verified Solution