sinx+siny=2sin(x+y2)cos(x−y2)\sin{x}+\sin{y}=2\sin{(\frac{x+y}{2})}\cos{(\frac{x-y}{2})}sinx+siny=2sin(2x+y)cos(2x−y)
sinx−siny=2cos(x+y2)sin(x−y2)\sin{x}-\sin{y}=2\cos{(\frac{x+y}{2})}\sin{(\frac{x-y}{2})}sinx−siny=2cos(2x+y)sin(2x−y)
cosx+cosy=2cos(x+y2)cos(x−y2)\cos{x}+\cos{y}=2\cos{(\frac{x+y}{2})}\cos{(\frac{x-y}{2})}cosx+cosy=2cos(2x+y)cos(2x−y)
cosx−cosy=2sin(x+y2)sin(x−y2)\cos{x}-\cos{y}=2\sin{(\frac{x+y}{2})}\sin{(\frac{x-y}{2})}cosx−cosy=2sin(2x+y)sin(2x−y)