Question

How do you solve `tan 1/2x + 2 sin 2x = csc x`?

Answer 1

The question is not clear enough.

I can only suggest a way to solve this equation.

Call `tan (x/2) = t`. Replace sin x and cos x in terms of t.

`2sin 2x = 4sin x.cos x = 4((2t)/(1 + t^2))((1 - t^2)/(1 + t^2))`

`csc x = 1/sin x = (2t)/(1 + t^2).`

Next solve for `t = tan (x/2)`