Prove the following:
sin(x+y)sin(x-y) = cos^2 (y) - cos^2 (x)
sin A sin B = ½ cos(A−B) − ½ cos(A+B)
sin(x+y)sin(x-y) =
1/2 [cos(2y) - cos(2x)]
1/2 (2cos^2(y)-1 - 2cos^2(x)+1)
cos^2(y) - cos^2(x)
sin(x+y)sin(x-y) = cos^2 (y) - cos^2 (x)
sin(x+y)sin(x-y) =
1/2 [cos(2y) - cos(2x)]
1/2 (2cos^2(y)-1 - 2cos^2(x)+1)
cos^2(y) - cos^2(x)