法国香水电影:求证:sin(α+β)sin(α-β)=sin²α-sin²β
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sin(α+β)sin(α-β)
=[sinαcosβ+cosαsinβ][sinαcosβ-cosαsinβ]
=[sinαcosβ]^2-sinαcosβcosαsinβ+cosαsinβsinαcosβ-[cosαsinβ]^2
=[sinαcosβ]^2-[cosαsinβ]^2
=[sinα]^2[1-(sinβ)^2]-[1-(sinα)^2][sinβ]^2
=[sinα]^2-[sinα]^2(sinβ)^2-[sinβ]^2+(sinα)^2][sinβ]^2
=[sinα]^2-[sinβ]^2
求证:sin(α+β)sin(α-β)=sin²α-sin²β
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求解:3sinβ=sin(2α+β),求证tan(α+β)=2tanα
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