1 - sin 2x = cos x - sin x

Square both sides:

(1−sin2x)^2=(cosx−sinx)2
1−2sin2x+(sin2x)^2=(cosx)^2+(sinx)^2−2sinxcosx
1−2sin2x+(sin2x)^2=1−sin2x
(sin2x)^2−sin(2x)=0
sin 2x (sin 2x - 1) = 0

a. sin 2x = 0
sin 2x= 0 --> 2x = 0 --> x = 0
sin 2x = 0 --> 2x=π --> x=π/2
sin 2x = 0 --> 2x=2π --> x=π

b. sin 2x = 1 --> 2x=π/2 --> x=π/4