sin(a+b)sin(a-b)
=(sinacosb+cosasinb)(sinacosb-cosasinb)
=sin^2acos^2b-cos^2asin^2b
=(1-cos^2a)cos^2b-cos^2a(1-cos^2b)
=cos^2b-cos^2acos^2b-cos^2a+cos^2acos^2b
=cos^2b-cos^2a
sin(a+b)sin(a-b)
=(sinacosb+cosasinb)(sinacosb-cosasinb)
=sin^2acos^2b-cos^2asin^2b
=(1-cos^2a)cos^2b-cos^2a(1-cos^2b)
=cos^2b-cos^2acos^2b-cos^2a+cos^2acos^2b
=cos^2b-cos^2a