What is 2sin(x)=tan(x/2)?

Assume that 0° ≤ x ≤ 360°
i.e. 0° ≤ x/2 ≤ 180°

Identity used: sin(x) = 2 sin(x/2) cos(x/2)

2 sin(x) = tan(x/2)
2 [2 sin(x/2) cos(x/2)] = sin(x/2) / cos(x/2)
4 sin(x/2) cos²(x/2) = sin(x/2)
4 sin(x/2) cos²(x/2) - sin(x/2) = 0
sin(x/2) [4 cos²(x/2) - 1] = 0
sin(x/2) = 0 or 4 cos²(x/2) = 1
sin(x/2) = 0 or cos(x/2) = 1/2 or cos(x/2) = -1/2
x/2 = 0°, 180° or x/2 = 60° or x/2 = (180-60)°
x/2 = 0°, 60°, 120°, 180°
x = 0°, 120°, 240°, 360°

First, can you sate here the half angle identity ?
Type it here and then we will show you how to apply it.