Question

If A = 60°, B = 30°, verify that sin(A + B) = sin A cos B + cos A sin B.

Answer 1

We have, A = 60°, B = 30° and sin(A + B) = sin A cos B + cos A sin B

LHS = sin(A + B)

= sin(60° + 30°) = sin 90° = 1

RHS = sin A cos B + cos A sin B

= sin 60° cos 30° + cos 60° sin 30°

= \(\frac{\sqrt3}{2}\) × \(\frac{\sqrt3}{2}\) + \(\frac{1}{2}\) × \(\frac{1}{2}\) = \(\frac{3}{4}\) + \(\frac{1}{4}\) = 1

∴ LHS = RHS