The period of the function f(x)=tan⁡x is

Let f(T + x) = f (x)⇒tan⁡(T+x)=tan⁡x⇒tan⁡(T+x)=tan⁡x⇒T+x=nπ+x,n∈ZClearly, from here, the least positive value of T independent of x is π. Therefore, f (x) is a periodic function of period π.