sin(B+C)sin(B-C)=(sinBcosC+cosBsinC)(sinBcosC-cosBsinC)=sin^2Bcos^2C-cos^2Bsin^2C
=sin^2B(1-sin^2C)-(1-sin^2B)sin^2C=sin^2B-sin^2C;
cos(B+C)cos(B-C)=(cosBcosC-sinBsinC)(cosBcosC+sinBsinC)=cos^2Bcos^2C-sin^2Bsin^2C
=cos^2Bcos^2C-(1-cos^2B)(1-cos^2C)=cos^2B-cos^2C.