Question

Is the function f defined by f(x) = tan(2x) is a periodic function with period π

Answer 1

Taking into account that the smallest period of the function $\tan(x)$ is $\pi,$ we conclude that the smallest period of the function $f(x) = \tan(2x)$ is $\frac{\pi}2.$ Since $\pi=2\cdot\frac{\pi}2,$ we conclude that $\pi$ is also a period of $f,$ but it is not the smallest period.