sinx+2=2cos^2 x?

Question

i need this as soon as possible please im really stuck

Answer 1

sin x + 2 = 2 cos² x
sin x + 2 = 2(1 - sin² x)
sin x + 2 = 2 - 2sin² x
2sin² x + sin x = 0
(sin x)(2sin x + 1) = 0
sin x = 0
x = 0 + 2πn or x = π + 2πn
or
2sin x + 1 = 0
sin x = -1/2
x = 7π/6 + 2πn or x = 11π/6 + 2πn