]sin3x=\sqrt{2}cosx-sinx

 3sin(x) cos^2 (x)-sin^3(x)=\sqrt{2} cos(x)-sin(x)

 sin(x)(2 cos(2x)+1)=\sqrt{2} cos(x)-sin(x)

 sin(x)+sin(3x)=\sqrt{2} cos(x)