当cos^2x-cos^2y=√3/2时,求sin(x+y)×sin(x-y)
问题描述:
当cos^2x-cos^2y=√3/2时,求sin(x+y)×sin(x-y)
答
∵ cos^2x-cos^2y=(cosx-cosy)(cosx+cosy=)= -2(sin(x/2-y/2))(sin(x/2+y/2))(cos(x/2-y/2))(cos(x/2+y/2))= -sin
(x-y)sin(x+y)=√3/2∴sin(x-y)sin(x+y) = -√3/2