First what we need to do is to reduce the given equation to the quadratic equation for sin(x).
For it, use the identity cos^2(x) = 1-sin^2(x) and replace cos^2(x) in the equation by this expression. You will get

2*(1-sin^2(x) + sin(x) - 1 = 0,   or

2 - 2sin^2(x) + sin(x) - 1 = 0,   or

2sin^2(x) - sin(x) - 1 = 0.

Factor left side:

(2sin(x) + 1)*(sin(x) - 1) = 0.

Now the equation deploys in two independent equations:


1.  2sin(x) + 1 = 0  --->  sin(x) =   --->  x =   and/or  x = .


2.  sin(x) - 1 = 0  --->  sin(x) = 1  --->  x = .


Answer.  The solutions are  x = ,   and  .