By, means of an example, show that sin(A + B) ≠ sin A + sin B.

If θ = 30°, verify that

(i) sin 2θ = 2 sin θ cos θ

(ii) cos 2θ = 2 cos² θ - 1

(iii) sin 3θ = 3 sin θ - 4 sin³ θ

(iv) cos 3θ = 4 cos³ θ - 3 cos θ