Question

(Prove that):
2 sin 7A. cos 2A = sin 9A + sin 5A​

Answer 1

Below.

Explanation:

We use the identity:

sin A + sin B = 2 sin(A+B)/ 2 cos(A-B)/2

so sin 9A + cos 5A

= 2 sin (9A + 5A)/2 cos (9A - 5A)/2

= 2 sin 14/2 cos 4/2

= 2 sin7A cos 2A.