I came across a problem of finding period of function
$ \frac{tg^2(x)}{1+tgx}$
I tried to simplify it in terms of cosines and sines, but I didn't get anything I can work with. This is just an example of more general problem. What is theory behind finding periods of such functions (that are represented as fraction). I know that such function isn't always periodic and we can check that with $f(x+T) - f(x) = 0$, but if it is periodic I don't know what is general solution to finding such periods.
Thanks for help!