Prove the identity

Question

sin (3 pi/2 + x) + sin (3 pi/2 -x) = -2 cos x

Answer 1

Use the identities
sin (a + b) = sin a cos b + sin b cos a
sin (a - b) = sin a cos b - sin b cos a
and the facts that sin 3 pi/2 = -1 and cos 3 pi/2 = 0