find the general solution of cosx +sinx -sin2x=2

Question

It is a question of trigonometric equations solutions.To find the general solution.

Answer 1

It’s not clear whether the third term is sin(2x) or sin²(x), but the graph shows that whichever it is there can be no (real) solution:

The blue curve has sin(2x) as the third term, while the green curve has sin²(x). Neither periodic function reaches f(x)=2 but they both pass f(x)=-2, so there would be solutions if the right-hand side of the given equation was -2 instead of 2.