Find all solutions of the equation in the interval

Question

, 02π
.

=2sin2x−2cosx
Write your answer in radians in terms of
π
.
If there is more than one solution, separate them with commas.

Answer 1

I assume you mean

2sin2x - 2cosx = 0
4sinx cosx - 2cosx = 0
2cosx(2sinx-1) = 0

so,
cosx = 0
or
sinx = 1/2

so, there will be four solutions in [0,2π)