\(\sin{x}+\sin{y}=2\sin{(\frac{x+y}{2})}\cos{(\frac{x-y}{2})}\)
\(\sin{x}-\sin{y}=2\cos{(\frac{x+y}{2})}\sin{(\frac{x-y}{2})}\)
\(\cos{x}+\cos{y}=2\cos{(\frac{x+y}{2})}\cos{(\frac{x-y}{2})}\)
\(\cos{x}-\cos{y}=2\sin{(\frac{x+y}{2})}\sin{(\frac{x-y}{2})}\)