化简:sin^2αcos^2β-cos^2αsin^2β+cos^2α-cos^2β具体步骤,

问题描述:

化简:sin^2αcos^2β-cos^2αsin^2β+cos^2α-cos^2β具体步骤,

sin^2αcos^2β-cos^2αsin^2β+cos^2α-cos^2β
=sin^2αcos^2β-cos^2β-cos^2αsin^2β+cos^2α
=(sin^2α-1)cos^2β-cos^2α(sin^2β-1)
=-(1-sin^2α)cos^2β+cos^2α(1-sin^2β)
=-cos^2αcos^2β+cos^2αcos^2β
=0