* If I have a function f(x) that is periodic with period p, then I know f(x+p) = f(x) for all x (by definition).

* If I have another function g(x) (which may or may not be periodic) and then consider the composition h(x) := g(f(x)), I can observe that

>h(x+p) = g(f(x+p)) = g(f(x)) = h(x), for all x.

* So I know that this composition h *is periodic* (or constant) and its period is *at most* p.

* If g isn't periodic itself, then the period of h will just be p.

Does that help at all? Can you break 2^(tan(x)) down into the composition of two functions, where one of them is periodic?