化简sin^2α+sin^2β-sin^2αsin^2β+cos^2αcos^2β

化简sin^2α+sin^2β-sin^2αsin^2β+cos^2αcos^2β

结果等于1
=sin^2a(1-sin^2β)+sin^2β+cos^2αcos^2β
=sin^2acos^2β+sin^2β+cos^2αcos^2β
=cos^2β(1-cos^β)+sin^2β
=cos^2β+sin^2β=1

上式=（sin^2α-sin^2αsin^2β）+sin^2β+cos^2αcos^2β =（sin^2α-sin^2αsin^2β）+1-cos^2β+cos^2αcos^2β =（sin^2α-sin^2αsin^2β）+1+（cos^2αcos^2β-cos^2β） =sin^2α（1-sin^2β）+1+cos^2β（cos^2β-1） =sin^2αcos^2β+1-cos^2βsin^2α =1+（sinαcosβ-cosβsinα）*（sinαcosβ+cosβsinα） =1+sin（α-β）*sin（α+β）

sin^2α+sin^2β-sin^2αsin^2β+cos^2αcos^2β =sin^2α+sin^2β(1-sin^2α)+cos^2αcos^2β =sin^2α+sin^2βcos^2α+cos^2αcos^2β =sin^2α+cos^2α(sin^2β+cos^2β) =sin^2α+cos^2α =1

你应该见过下面两组公式吧？！这个都转不过来，还怎么去高考啊~每方面的知识自己都得多练习练习一下才行啊 积化和差： sinαsinβ=-[cos(α+β)-cos(α-β)]/2 cosαcosβ=[cos(α+β)+cos(α-β)]/2 sinαcosβ=[sin(α+β)+sin(α-β)]/2 cosαsinβ=[sin(α+β)-sin(α-β)]/2 和差化积： sinθ+sinφ=2sin[(θ+φ)/2]cos[(θ-φ)/2] sinθ-sinφ=2cos[(θ+φ)/2]sin[(θ-φ)/2] cosθ+cosφ=2cos[(θ+φ)/2]cos[(θ-φ)/2] cosθ-cosφ=-2sin[(θ+φ)/2]sin[(θ-φ)/2]

sin^2α-sin^2αsin^2β+sin^2β+cos^2αcos^2β. =sin^2α-（1-cos^2α）（1-cos^2β） +sin^2β+cos^2αcos^2β =sin^2α-1+cos^2α+cos^2β-cos^2αcos^2β+sin^2β+cos^2αcos^2β =1

sin^2α+sin^2β-sin^2αsin^2β+cos^2αcos^2β =sin^2α(1-sin^2β)+sin^2β+cos^2αcos^2β =sin^2αcos^2β+sin^2β+cos^2αcos^2β =cos^2β(sin^2α+cos^2α)+sin^2β =cos^2β+sin^2β =1