TrigExpand@Tan[x + y]
gives
$\frac{\sin (x) \cos (y)}{\cos (x) \cos (y)-\sin (x) \sin (y)}+\frac{\cos (x) \sin (y)}{\cos (x) \cos (y)-\sin (x) \sin (y)}$
but my excepted result is
$\frac{\tan (x)+\tan (y)}{1-\tan (x) \tan (y)}$
On the $\tan (x-y)$ or $\tan (3*x)$ is also the case, What should I do?