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