cos方α-cos方β=a 求sin(α+β)*sin(α-β)

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cos方α-cos方β=a 求sin(α+β)*sin(α-β)

sin(α+β)*cos(α-β)=(sinαcosβ-cosαsinβ)(sinαcosβ+cosαsinβ)
=(sinα)^2*(cosβ)^2-(cosα)^2*(sinβ)^2
=(cosβ)^2-(cosα)^2*(cosβ)^2-(cosα)^2+(cosα)^2*(cosβ)^2
=(cosβ)^2-(cosα)^2=-a