Question

find all solutions of 2-2cos^2x=sinx+1

Answer 1

well make the substitution for cos^2 = 1 - sin^2

so you have

2 - 2(1 - sin^2(x)) = sin(x) + 1

which becomes after simplifying and rewriting

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

which is a quadratic that can be factored.

when you have the factors, you can solve for x.