已知sin(α+β)=2/3,sin(α-β)=1/5,求sin2αsin2β的值
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已知sin(α+β)=2/3,sin(α-β)=1/5,求sin2αsin2β的值
sin(α+β) = sinαcosβ+cosαsinβ = 2/3 . (1)
sin(α-β) = sinαcosβ-cosαsinβ = 1/5 . (2)
(1)+(2)得:2sinαcosβ = (2/3+1/5)
(1)-(2)得:2cosαsinβ = (2/3-1/5)
sin2αsin2β = 2sinαcosα * 2sinβcosβ = 2sinαcosβ * 2cosαsinβ = (2/3+1/5)(2/3-1/5) = 91/225
sin(α-β) = sinαcosβ-cosαsinβ = 1/5 . (2)
(1)+(2)得:2sinαcosβ = (2/3+1/5)
(1)-(2)得:2cosαsinβ = (2/3-1/5)
sin2αsin2β = 2sinαcosα * 2sinβcosβ = 2sinαcosβ * 2cosαsinβ = (2/3+1/5)(2/3-1/5) = 91/225
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