sinA+sinB = 2 sin[(A+B)/2] * cos[(A-B)/2]
sinA-sinB = 2 cos[(A+B)/2] * sin[(A-B)/2]
cosA+cosB = 2 cos[(A+B)/2] * cos[(A-B)/2]
cosA-cosB = -2 sin[(A+B)/2] * sin[(A-B)/2]
sinA+sinB = 2 sin[(A+B)/2] * cos[(A-B)/2]
sinA-sinB = 2 cos[(A+B)/2] * sin[(A-B)/2]
cosA+cosB = 2 cos[(A+B)/2] * cos[(A-B)/2]
cosA-cosB = -2 sin[(A+B)/2] * sin[(A-B)/2]