Please solve sin^2x+cosx=2

Question

Find all solutions between [0,2π).

 

Thank you

 

Answer 1

2 = sin² x + cos x

 

2 = 1 - cos² x + cos x

 

cos² x - cos x + 1 = 0

 

cos x = (-1 ± i√3)/2

 

These are not real numbers, so there is no real solution.