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?

Two related integrals:
$$\int_0^\infty\sin\;x\quad\mathrm{d}x=1$$
$$\int_0^\infty\ln\;x\;\sin\;x\quad \mathrm{d}x=-\gamma$$
