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?

$\tan^{-1}(1)+\tan^{-1}(2)+\tan^{-1}(3) = \pi$
(using the principal value),
but if you blindly use the addition formula
$\tan^{-1}(x) + \tan^{-1}(y)
= \tan^{-1}\dfrac{x+y}{1-x y}$
twice, you get zero:
$\tan^{-1}(1) + \tan^{-1}(2) =
\tan^{-1}\dfrac{1+2}{1-1*2}
=\tan^{-1}(-3)$;
$\tan^{-1}(1) + \tan^{-1}(2) + \tan^{-1}(3)
=\tan^{-1}(-3) + \tan^{-1}(3)
=\tan^{-1}\dfrac{-3+3}{1-(-3)(3)}
= 0$.
