By, means of an example, show that sin(A + B) ≠ sin A + sin B.
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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
If θ = 30°, find the ratio 2 sin θ : sin 2θ.