# Sum To Product Identities

## Reference > Algebra: Trigonometric Identities

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