2 sinx + cotx = cscx solve for x

solve for x in radians

Multiplying the entire equation by sin,

2 sin^2 + cos = 1 iff
2(1 - cos^2) + cos = 1 iff
2 - 2 cos^2 + cos = 1 iff
2 cos^2 - cos -1 = 0 iff
(2 cos + 1)(cos - 1) = 0 iff
cos x = -1/2 or cos x = 1

cos x = -1/2 when x = 2pi / 3 or x = 4pi / 3

cos x = 1 when x = 0 but csc x is undefined at this value.

Thus x = 2pi/3 or x = 4pi/3.