Double angle identity for sine:
sin(2x) = 2 sin(x) cos(x)
So rewrite the equation as
sin(2x) = cos(x)
2 sin(x) cos(x) = cos(x)
2 sin(x) cos(x) - cos(x) = 0
cos(x) (2 sin(x) - 1) = 0
There are two cases,
cos(x) = 0 or 2 sin(x) - 1 = 0
cos(x) = 0 or sin(x) = 1/2
In the interval 0º ≤ x < 180º, we have cos(90º) = 0 and sin(30º) = sin(150º) = 1/2, so the possible values are 30º, 90º, or 150º.
