sina+sinb=2sin1/2(a+b)*cos1/2(a-b)
sina-sinb=2cos1/2(a+b)*sin1/2(a-b)
cosa+cosb=2cos1/2(a+b)*cos1/2(a-b)
cosa-cosb=-2sin1/2(a+b)*sin1/2(a-b)