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