Product to Sum and Sum to Product

sin A cos B = ½ [sin (A + B) + cos (A – B)] sinA + sinB = 2 sin([A + B]/2)cos([A+B]/2)

cos A cos B = ½ [ cos (A - B) + cos (A + B)] sin A – sin B = 2 sin([A-B]/2)cos([A+B]/2)

sin A sin B = ½ [ cos (A - B) - cos (A + B)] cos A + cos B = 2 cos([A + B]/2)cos([A – B]/2)

cos A – cos B = 2 sin([A + B]/2)sin([A – B]/2)