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Question
Prove that:
sin 38° + sin 22° = sin 82°
Solution
Consider LHS:
\[\sin 38^\circ + \sin 22^\circ\]
\[ = 2\sin \left( \frac{38^\circ + 22^\circ}{2} \right) \cos \left( \frac{38^\circ - 22^\circ}{2} \right) \left\{ \because \sin A + \sin B = 2\sin \left( \frac{A + B}{2} \right) \cos \left( \frac{A - B}{2} \right) \right\}\]
\[ = 2\sin 30^\circ \cos 8^\circ\]
\[ = 2 \times \frac{1}{2}\cos(90^\circ - 8^\circ)\]
\[ = \sin 82^\circ\]
= RHS
Hence, LHS = RHS .
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