Sum-To-Product Identities

	$\displaystyle \sin x+\sin y=2\sin\left(\frac{x+y}{2}\right)\cos\left(\frac{x-y}{2}\right)$
	$\displaystyle \sin x-\sin y=2\cos\left(\frac{x+y}{2}\right)\sin\left(\frac{x-y}{2}\right)$
	$\displaystyle \cos x+\cos y=2\cos\left(\frac{x+y}{2}\right)\cos\left(\frac{x-y}{2}\right)$
	$\displaystyle \cos x-\cos y= -2\sin\left(\frac{x+y}{2}\right)\sin\left(\frac{x-y}{2}\right)$