Find all values of x such that sin 2x = sin x and 0 ≤ x ≤ 2π.

Hello:

sin 2x = sin x and 0 ≤ x ≤ 2π.

all solutions:

2x = x + 2k π or x = π - x + 2kπ ... k in : Z

x = 2kπ or : x = π/2 + kπ

but:

0 ≤ x ≤ 2π

all values of x such that sin 2x = sin x and 0 ≤ x ≤ 2π are:

k = 0 : x=0, x = π/2

k=1 : x=2 π, x=3π/2