证明sin^2α+sin^2β-sin^2α×sin^2β+cos^2α×cos^2β=1

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证明sin^2α+sin^2β-sin^2α×sin^2β+cos^2α×cos^2β=1证明sin^2α+sin^2β-sin^2α×sin^2β+cos^2α×cos^2β=1证明sin^2α+s

证明sin^2α+sin^2β-sin^2α×sin^2β+cos^2α×cos^2β=1
证明sin^2α+sin^2β-sin^2α×sin^2β+cos^2α×cos^2β=1

证明sin^2α+sin^2β-sin^2α×sin^2β+cos^2α×cos^2β=1
(sinα)^2+(sinβ)^2-(sinαsinβ)^2+(cosαcosβ)^2 =(1-cos2α)/2+(1-cos2β)/2+[cosαcosβ+sinαsinβ][cosαcosβ-sinαsinβ =1-1/2(cos2α+cos2β)+cos(α-β)cos(α+β) =1-1/2*2cos(α-β)cos(α+β)+cos(α-β)cos(α+β) =1
求采纳

sinα+sinβ-sinα×sinβ+cosα×cosβ =sinα(1-sinβ)+sinβ+cosα×cosβ =sinαcosβ+sinβ+cosα×cosβ =cosβ(sinα+cosα)+sinβ =cosβ+sinβ =1