Condition of the problem

Calculate the limit of the function:

$\lim _{x \rightarrow \frac{\pi}{4}}(\operatorname{tg} x)^{\operatorname{ctg} x}$
Solution

$\lim _{x \rightarrow \frac{\pi}{4}}(\tan x)^{\cot x}=(\tan \frac{\pi}{4})^{\cot \frac{\pi}{4}}=1^{1}=1$

## Problem Kuznetsov Limits 20-2