cosα(cosα－cosβ)+ sinα(sinα－sinβ)
=cos²α-cosαcosβ+sin²α-sinαsinβ
=1-(cosαcosβ+sinαsinβ)
=1-cos(α-β)
=1-[1-2sin²(α-β)/2]
=2sin²(α-β)/2
得证.