Question

Sin(150 + x)+ sin(150 − x) = cos x

Answer 1

Below.

Explanation:

We need to prove this identity by taking the left side and trying to transform it to the right side.

LHS = sin(150 + x) + sin(150 − x)

= sin 150 cos x + sin x cos 150 + sin 150 cos x - sin x cos 150

= 2 sin 150 cos x

= 2 * 1/2 * cos x

= cos x = RHS.

So it is proved.