和積公式

参照 > 代数学: 三角関数の公式

説明

sinx+siny=2sin(x+y2)cos(xy2)\sin{x}+\sin{y}=2\sin{(\frac{x+y}{2})}\cos{(\frac{x-y}{2})}

sinxsiny=2cos(x+y2)sin(xy2)\sin{x}-\sin{y}=2\cos{(\frac{x+y}{2})}\sin{(\frac{x-y}{2})}

cosx+cosy=2cos(x+y2)cos(xy2)\cos{x}+\cos{y}=2\cos{(\frac{x+y}{2})}\cos{(\frac{x-y}{2})}

cosxcosy=2sin(x+y2)sin(xy2)\cos{x}-\cos{y}=2\sin{(\frac{x+y}{2})}\sin{(\frac{x-y}{2})}