f（x）=cos（2x-π/3）+2sin（x-π/4）sin（x+π/4）
=1/2cos 2x+根号3/2sin 2x+2*(根号2/2sin x-根号2/2cos x)(根号2/2sin x+根号2/2cos x)
=1/2cos 2x+根号3/2sin 2x+ 2*根号2/2 * 根号2/2 *(sin x+cos x)(sin x-cos x)
=1/2cos 2x+根号3/2sin 2x+ 2+(sin^2 x-cos^2 x)
=1/2cos 2x+根号3/2sin 2x+ 2-cos 2x
=根号3/2 sin 2x-1/2 cos 2x
=sin 2x cos π/6-cos 2x sin π/6
=sin(2x-π/6)