How to find the period of $ (\tan x )^{0.45}$? How to find the period of $(\tan x)^{0.45}$?
I know the period of $\tan x$ is $\pi$.  Can anyone please help me?

$\pi$. You do not change periodicity by raising to this particular power.
Obviously $(\tan(x+\pi))^{0.45}= (\tan(x))^{0.45}$. So all you need to check if there is not a shorter period. But where $\tan$ is positive, so your function is defined, the function is increasing in each smaller than $\pi$ interval, so it cannot have smaller periodicity.
