化简sin^2α+sin^2β+2sinαsinβcos(α+β)
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/08/23 21:47:41
化简sin^2α+sin^2β+2sinαsinβcos(α+β)
sin^2α+sin^2β+2sinαsinβcos(α+β)
=1/2(1-cos2α)+1/2(1-cos2β)+
2sinαsinβ(cosαcosβ-sinαsinβ)
=1/2(1-cos2α)+1/2(1-cos2β)+
2sinαcosαsinβcosβ-2sinαsinβsinαsinβ=1/2(1-cos2α)+1/2(1-cos2β)+
1/2sin2αsin2β-2sin^2αsin^2β=1-1/2cos2α-1/2cos2β+1/2sin2αsin2β-1/2(1-cos2α)(1-cos2β)=1-1/2cos2α-1/2cos2β+1/2sin2αsin2β-1/2+1/2cos2α+1/2cos2β-1/2cos2αcos2β=1/2-1/2(cos2αcos2β-sin2αsin2β)=1/2-1/2cos(2α+2β)
=1/2(1-cos2α)+1/2(1-cos2β)+
2sinαsinβ(cosαcosβ-sinαsinβ)
=1/2(1-cos2α)+1/2(1-cos2β)+
2sinαcosαsinβcosβ-2sinαsinβsinαsinβ=1/2(1-cos2α)+1/2(1-cos2β)+
1/2sin2αsin2β-2sin^2αsin^2β=1-1/2cos2α-1/2cos2β+1/2sin2αsin2β-1/2(1-cos2α)(1-cos2β)=1-1/2cos2α-1/2cos2β+1/2sin2αsin2β-1/2+1/2cos2α+1/2cos2β-1/2cos2αcos2β=1/2-1/2(cos2αcos2β-sin2αsin2β)=1/2-1/2cos(2α+2β)
化简:(1)sin(α+β)−2sinαcosβ2sinαsinβ+cos(α+β)
化简:sin(α+β)-2sinαcosβ/2sinαsinβ+cos(α+β)
化简sin^2α+sin^2β-sin^2αsin^2β+cos^2cos^2β
求证sin^2α+sin^2β-sin^2αsin^2β+cos^2cos^2β=1
求证sinα-sinβ=2cos(α+β)/2sin(α-β)/2
求证 sinαcosβ=1/2[sin(α+β)+sin(α-β)]
求证:[sin(2α+β)/2sinα]-cos(α+β)=sinβ/2sinα
求证:sin(2α+β)sinα
sinα^2+sinβ^2+sinγ^2=1,那么cosαcosβcosγ最大值等于
sin(α+β)=2/3,sin(α-β)=3/5,sinα+sinβ=1/2,求cos(α+β)/2*sin(α-β)
已知sin(α+β)=2/3,sin(α-β)=3/5,sinα+sinβ=1/2,求cos[(α+β)/2]*sin[
若α β是锐角tanβ=sinα -cosα / sinα + cosα 求证sinα -cosα=根号2sinβ