Question

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

Answer 1

只枣毕启有最后数笑1项中有cos，所以把cos化为sin
最后1项 cos^2αcos^2β=（1-sin^2α）*（1-sin^2β）凳如=1-sin^2β-sin^2α+sin^2αsin^2β

代入原式，得：原式=1

Answer 2

你应该见过下面两组公式吧？！这迹敬个都转不过来，还怎么去高考啊~每方面的知识自己都得多练习练习毕州闹一下才行啊

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)]/手罩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]

Answer 3

上式洞昌=（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（晌森α-β）*sin（α+β）宴颤亩

Answer 4

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

Answer 5

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