作业帮sinθ-cosθ=1/2,则sin^3θ-cos^3θ=?.
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/03 09:00:44
sinθ-cosθ=1/2,则sin^3θ-cos^3θ=?.
sinθ-cosθ=1/2,则sin^3θ-cos^3θ=?.
sinθ-cosθ=1/2,则sin^3θ-cos^3θ=?.
sin^3θ-cos^3θ=(sin^θ-cos^θ)(sin^2θ+sin^θcos^θ+cos^2θ)
sinθ-cosθ=1/2,(sinθ-cosθ)^2=sin^2θ-2sin^θcos^θ+cos^2θ=1-2sin^θcos^θ=1/4
sin^θcos^θ=3/8
sin^3θ-cos^3θ=(sin^θ-cos^θ)(sin^2θ+sin^θcos^θ+cos^2θ)
=1/2*(1+3/8)=11/16
首先你要知道1=sin^2X+COS^2X
1 sin^3x-cos^3x=(sinx-cosx)(1+sinx*cosx);
2 -sinx*cosx=((sinx-cosx)^2-1)/2;sinxcosx=3/8;
3 所以原式=1/2*11/8=11/16
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