已知cos²α-cos²β=1/3,那么sin(α+β)·sin(α-β)=
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已知cos²α-cos²β=1/3,那么sin(α+β)·sin(α-β)=
已知cos²α-cos²β=1/3,那么sin(α+β)·sin(α-β)=
已知cos²α-cos²β=1/3,那么sin(α+β)·sin(α-β)=
sin(α+β)=sinαcosβ+cosαsinβ
sin(α-β)=sinαcosβ-cosαsinβ
sin(α+β)*sin(α-β)=sinα²cosβ²-cosα²sinβ²
=(1-cosα²)cosβ²-cosα²(1-cosβ²)
=cosβ²-cosα²cosβ²-cosα²+cosα²cosβ²
=cosβ²-cosα²
因为 cos²α-cos²β=1/3
所以 cosβ²-cosα²=-1/3
sin(α+β)*sin(α-β)=-1/3