已知sin(α+β)*sin(α-β)=-1/3,求sin^2α-sin^2β的值

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已知sin(α+β)*sin(α-β)=-1/3,求sin^2α-sin^2β的值

已知sin(α+β)*sin(α-β)=-1/3,求sin^2α-sin^2β的值
已知sin(α+β)*sin(α-β)=-1/3,求sin^2α-sin^2β的值

已知sin(α+β)*sin(α-β)=-1/3,求sin^2α-sin^2β的值
sin(α+β)*sin(α-β)=(sinαcosβ)^2-(cosαsinβ)^2=-1/3
(1-sin^2β)sin^2α-(1-sin^2α)sin^2β=-1/3
sin^2α-sin^2βsin^2α-sin^2β+sin^2αsin^2β=-1/3
sin^2α-sin^2β=-1/3