求证:sin(a+b)sin(a-b)=sin^2a-sin^2b
问题描述：
求证:sin(a+b)sin(a-b)=sin^2a-sin^2b
答
sin(A+B)sin(A-B)
=(sinacosb+sinbcosa)(sinacosb-sinbcosa)
=sin^2acos^2b-sin^2bcos^2a
=sin^2a(1-sin^2b)-sin^2b(1-sin^2a)
=sin^2a-sin^2asin^2b-sin^2b+sin^2bsin^2a
=sin^2a-sin^2b