QJEEM21Maae7b: JEE Main 2021 Mathematics - Class 12 JEEM21Maae7b Solution: A possible value of is :

Question

Verified Solution • 2025–26 Session moderate

A possible value of

\tan \left( {{1 \over 4}{{\sin }^{ - 1}}{{\sqrt {63} } \over 8}} \right)

is :

Accepted Answer

\tan \left( {{1 \over 4}{{\sin }^{ - 1}}{{\sqrt {63} } \over 8}} \right)

{\sin ^{ - 1}}\left( {{{\sqrt {63} } \over 8}} \right) = \theta

\sin \theta = {{\sqrt {63} } \over 8}

\cos \theta = {1 \over 8}

2{\cos ^2}{\theta \over 2} - 1 = {1 \over 8}

{\cos ^2}{\theta \over 2} = {9 \over {16}}

\cos {\theta \over 2} = {3 \over 4}

{{1 - {{\tan }^2}{\theta \over 4}} \over {1 + {{\tan }^2}{\theta \over 4}}} = {3 \over 4}

\tan {\theta \over 4} = {1 \over {\sqrt 7 }}

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