rewrite the equation cos x=2 - 2sin x

square both sides and substitute cos^2 x = 1- sin^2 x
we get 5 sin^2 x- 8 sin x+5 =0
by factoring we have sinx=3/5 or sin x= 1

s0 x = k pi /2 where k is odd integer or sin^-1 3/5 +2k pi k is integer or pi - sin^-13/5 + 2 k pi