若θ角是锐角,sinθ-cosθ=1/2,求sin^3θ-cos^3θ

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若θ角是锐角,sinθ-cosθ=1/2,求sin^3θ-cos^3θ
若θ角是锐角,sinθ-cosθ=1/2,求sin^3θ-cos^3θ

若θ角是锐角,sinθ-cosθ=1/2,求sin^3θ-cos^3θ
sinθ-cosθ=1/2
(sinθ-cosθ)^2=1/4
1-2sinθcosθ=1/4
sinθcosθ=3/8
sin^3θ-cos^3θ
=(sinθ-cosθ)(sin^2θ+sinθcosθ+cos^2θ)
=(1+sinθcosθ)/2
=(1+3/8)/2
=11/16