Find all solutions of the given equation in the interval [0,2n)

Question

Find all solutions of the given equation in the interval [0,2n)

1/2 sin 2x = cos x

Answer 1

From double angle identity, 1/2 sin 2x = 1/2 (2 sin x cos x). Then sin x cos x = cos x leaving sin x = 1 which occurs of course at π/2.