已知sinx-cosx=根号2/2,求sinx的3次方-cosx的3次方的值

(sin x-cos x)^2
=1/2
=sin^2 x+cos^2 x+2 sin x*cos x
=1+2 sin x*cos x
∴sinx*cosx=-1/4
sin^3 x -cos^3 x
=(sin x -cos x )(sin^2 x +sin x*cos x +cos^2 x )
=(sin x -cos x )(1+sin x*cos x )
=（√2/2）(1-1/4)=(3√2)/8
答案自己在验算一遍