cos2(x)-sin2(x)=sin(x);
1-2sin2(x)=sin(x);
2sin2(x)+sin(x)-1=0=(2sin(x)-1)(sin(x)+1).
Therefore sin(x)=½; or sin(x)=-1.
x=π/6 (30°), 5π/6 (150°); x=3π/2 (270°).
The more general answer is:
x=π/6+2nπ (30°+360n°), 5π/6+2nπ (150°+360n°), 3π/2+2nπ (270°+360n°) where n is an integer.