sin(α+β)*cos(α-β)=(sinαcosβ-cosαsinβ)(sinαcosβ+cosαsinβ)
=(sinα)^2*(cosβ)^2-(cosα)^2*(sinβ)^2
=(cosβ)^2-(cosα)^2*(cosβ)^2-(cosα)^2+(cosα)^2*(cosβ)^2
=(cosβ)^2-(cosα)^2=-a