Question

Prove that:
sin 50° + sin 10° = cos 20°

Answer 1

Consider LHS: 
\[\sin 50^\circ + \sin 10^\circ\]
\[ = 2\sin \left( \frac{50^\circ + 10^\circ}{2} \right) \cos \left( \frac{50^\circ - 10^\circ}{2} \right) \left\{ \because \sin A + \sin B = 2\sin \left( \frac{A + B}{2} \right) \cos \left( \frac{A - B}{2} \right) \right\}\]
\[ = 2\sin 30^\circ \cos 20^\circ\]
\[ = 2 \times \frac{1}{2}\cos 20^\circ\]
\[ = \cos 20^\circ\]
Hence, LHS = RHS .