Funny identities Here is a funny exercise 
$$\sin(x - y) \sin(x + y) = (\sin x - \sin y)(\sin x + \sin y).$$
(If you prove it don't publish it here please).
Do you have similar examples?

$$
\int_{-\infty}^{\infty}{\sin\left(x\right) \over x}\,{\rm d}x
=
\pi\int_{-1}^{1}\delta\left(k\right)\,{\rm d}k
$$
