sin（α+β）sin（α-β）=（sinαcosβ+cosαsinβ）（sinαcosβ-cosαsinβ）=（sinαcosβ）^2-(cosαsin β)^2=(1-cosαcosα)cos^2β-cos^2αsin^2β=cos^2β-cos^2αcos^2β-cos^2αsin^2β=cos^2β-cos^2α故得证
