cos^2a-cos^2b=m,那么sin(a+b)sin(a-b)=?

题目

cos^2a-cos^2b=m,那么sin(a+b)sin(a-b)=?

答案

sin(a+b)sin(a-b)
=-[cos(a+b+a-b)-cos(a+b-a+b)]/2
=(cos2b-cos2a)/2
={[2(cosb)^2-1]-[2(cosa)^2-1]}/2
=(cosb)^2-(cosa)^2
=-m