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已知sinθ-cosθ=1/2,则sin³θ-cis³θ=
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已知sinθ-cosθ=1/2,则sin³θ-cis³θ=
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答案和解析
sinθ-cosθ=1/2
(sinθ-cosθ)^2=1/4
sin^2θ+cos^2θ+2sinθcosθ=1/4
1+2sinθcosθ=1/4
2sinθcosθ=-3/4
sinθcosθ=-3/8
sin³θ-cos³θ
=(sinθ-cosθ)(sin^2θ+sinθcosθ+cos^2θ)
=1/2*(1-3/8)
=5/16
(sinθ-cosθ)^2=1/4
sin^2θ+cos^2θ+2sinθcosθ=1/4
1+2sinθcosθ=1/4
2sinθcosθ=-3/4
sinθcosθ=-3/8
sin³θ-cos³θ
=(sinθ-cosθ)(sin^2θ+sinθcosθ+cos^2θ)
=1/2*(1-3/8)
=5/16
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