sin(a+b)cos(a-b)
=(sinacosb+cosasinb)(cosacosb+sinasinb)
=sinacosa(cosb)^2+(sina)^2sinbcosb+(cosa)^2sinbcosb+(sinb)^2sinacosa
=sinacosa[(cosb)^2+(sinb)^2]+sinbcosb[(sina)^2+(cosa)^2]
=sinacosa*1+sinbcosb*1
=sinacosa+sinbcosb