sin(x+y)sin(x-y)=m,则cosx的平方-cosyd平方的值为?

Question

sin(x+y)sin(x-y)=m,则cosx的平方-cosyd 平方的值为?

Answer 1

sin(x+y)*sin(x-y)=m
(sinx*cosy+siny*cosx)*(sinx*cosy-siny*cosx)=m
(sinx*cosy)^2-(siny*cosx)^2=m
sin^2(x)*cos^2(y)-sin^2(y)*cos^2(x)=m
sin^2(x)*cos^2(y)-[1-cos^2(y)]*cos^2(x)=m
sin^2(x)*cos^2(y)-cos^2(x)+cos^2(y)*cos^2(x)=m
[sin^2(x)+cos^2(x)]*cos^2(y)-cos^2(x)=m
cos^2(y)-cos^2(x)=m
故：原式=-[cos^2(y)-cos^2(x)]=-m