cosx的平方-cosy的平方=0.25,那么sin(x+y)sin(x-y)的值

Question

cosx的平方-cosy的平方=0.25,那么sin(x+y)sin(x-y)的值

Answer 1

sin(x+y)sin(x-y)
=1/2(cos2y-cos2x) 用积化差公式sinx*siny=1/2(cos(x-y)-cos(x+y))
=1/2(2cosy^2-1-(2cosx^2-1)) 用余弦和角公式cos2x=cosx^2-sinx^2=cosx^2-(1-cosx^2)=2cosx^2-1
=cosy^2-cosx^2
=-1/4.