Question

一道高中三角数学题Cos2a---cos2b=c,则sin(a+b)sin(a---b)等于多少？？

RT
抱歉，打错了，2应该是平方，网页显示不上

Answer 1

sin(a+b)sin(a-b)
={cos[(a+b)+(a-b)]cos[(a+b)-(a-b)]}/2 积化和差
=-(cos2a-cos2b)/2
=-c/2

Answer 2

设a+b=A，a-b=B，cos2a-cos2b=cos(A+B)-cos(A-B)=-2sinAsinB=c.所以sin(a+b)sin(a-b)=-c/2