sin(A+B)sin(A-B)=?

Answer 1

sin(A+B)=sinAcosB+cosAsinB
sin(A-B)=sinAcosB-cosAsinB
sin(A+B)sin(A-B)=sin2^Acos2^B-cos2^Asin2^B

Answer 2

The formula for sin(a + b) is sin(a)cos(b) + sin(b)cos(a). Similarly, the formula for sin(a - b) is sin(a)cos(b) - sin(b)cos(a). Therefore,

sin(A + B)sin(A - B) =
[sin(A)cos(B) + sin(B)cos(A)][sin(A)cos(B) - sin(B)cos(A)]

As you can see, these are the product of conjugates, so our result should be a difference of squares and we should get

[sin(A)cos(B)]^2 - [sin(B)cos(A)]^2, or

sin^2(A)cos^2(B) - sin^2(B)cos^2(A)