QJEEM20Ma5d73: JEE Main 2020 Mathematics - Class 11 JEEM20Ma5d73 Solution: The value of + is :

Question

Verified Solution • 2025–26 Session moderate

The value of

{\cos ^3}\left( {{\pi \over 8}} \right)

{\cos}\left( {{3\pi \over 8}} \right)

+

{\sin ^3}\left( {{\pi \over 8}} \right)

{\sin}\left( {{3\pi \over 8}} \right)

is :

Accepted Answer

{\cos ^3}\left( {{\pi \over 8}} \right)

{\cos}\left( {{3\pi \over 8}} \right)

+

{\sin ^3}\left( {{\pi \over 8}} \right)

{\sin}\left( {{3\pi \over 8}} \right)

=

{\cos ^3}\left( {{\pi \over 8}} \right)\sin \left( {{\pi \over 8}} \right) + {\sin ^3}\left( {{\pi \over 8}} \right)\cos \left( {{\pi \over 8}} \right)

=

\sin \left( {{\pi \over 8}} \right)\cos \left( {{\pi \over 8}} \right)\left[ {{{\cos }^2}\left( {{\pi \over 8}} \right) + {{\sin }^2}\left( {{\pi \over 8}} \right)} \right]

=

\sin \left( {{\pi \over 8}} \right)\cos \left( {{\pi \over 8}} \right)

\times

1

=

{1 \over 2} \times 2\sin \left( {{\pi \over 8}} \right)\cos \left( {{\pi \over 8}} \right)

=

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

=

{1 \over {2\sqrt 2 }}

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