Answer
$$\lim _{x \rightarrow 0} \frac{\cot x}{\csc x}=1$$
Work Step by Step
Given $$\lim _{x \rightarrow 0} \frac{\cot x}{\csc x}$$
let $$ f(x) = \frac{\cot x}{\csc x}$$
Since, we have
$$ f(0)= \frac{\cot 0}{\csc 0}=\frac{0}{0}$$
So, transform algebraically and cancel, we get
\begin{aligned}
L&= \lim _{x \rightarrow 0} \frac{\cot x}{\csc x}\\
&= \lim _{x \rightarrow 0} \frac{\cos x}{\sin x} \frac{1}{\csc x}\\
&= \lim _{x \rightarrow 0} \frac{\cos x}{\sin x} \sin x \\
&= \lim _{x \rightarrow 0} \cos x\\
&=\cos 0\\
&=1
\end{aligned}
