Question

已知(cosA)^2-(cosB)^2=1,则sin（A+B）*sin（A-B）=?

Answer 1

sin(A+B)*sin(A-B)=-1/2(cos(A+B+A-B)-cos(A+B-A+B))=-1/2(cos2A-cos2B)=-1/2(2(cosA)^2-1-2(cosB)^2+1)=-1/2*2((cosA)^2-(cosB)^2)=-1/2*2*1=-1