# How to write sin (x+y) - sin (x-y) as a product?

$\sin \left(x + y\right) = \sin x \cos y + \cos x \cdot \sin y$
$\sin \left(x - y\right) = \sin x \cdot \cos y - \cos x \cdot \sin y$
$\sin \left(x + y\right) - \sin \left(x - y\right) = 2 \cdot \cos x \cdot \sin y$