Question

如何使1/2(cos2B-cos2A)=sin(A+B)sin(A-B)

Answer 1

2b=(a+b)-(a-b)

2a=(a+b)+(a-b)

原式=1/2[cos(a+b)cos(a-b)+sin(a+b)sin(a-b)-cos(a+b)cos(a-b)+sin(a+b)sin(a-b)]

=1/2[2sin(a+b)sin(a-b)]]

=sin(a+b)sin(a-b)