Question 226 of 298MediumMCQ
The value of cos38π⋅cos83π+sin38π⋅sin83π is:
Solutions · 1
Official solution
\[{\cos ^3}\left( {{\pi \over 8}} \right)\] {\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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