已知sinθ-cosθ=1/2,则sin³θ-cis³θ=
问题描述：
已知sinθ-cosθ=1/2,则sin³θ-cis³θ=
答
sinθ-cosθ=1/2(sinθ-cosθ)^2=1/4sin^2θ+cos^2θ+2sinθcosθ=1/41+2sinθcosθ=1/42sinθcosθ=-3/4sinθcosθ=-3/8sin³θ-cos³θ=(sinθ-cosθ)(sin^2θ+sinθcosθ+cos^2θ)=1/2*(1-3/8)=5/16