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**Period of trig functions!!**

This is a rather easy-silly quiestion but i just don't know how to show it.

I know how to find the period of trig functions of the form f(x)=Asin(wx+c) etc. i mean i know how to show that the period of this is [tex]\frac{2\pi}{w}[/tex].

However, how would one find the period of let's say the following function, is there any analitycal method of showing it:

[tex]f(x)=asin(wx+c)+kcos(f \pi x+d)-rtan(zx)[/tex]

Is there any way to prove it analiytically?

letters in front of x are constants.