How do you simplify the expression $\frac{1}{cotx}$?

Simplify the given expression

We know that, $cot\theta =\frac{\cos \theta }{\sin \theta }$

$\frac{1}{cotx}$ can be expressed in terms of $\sin x$ and $\cos x$ as

$$\begin{gathered} \frac{1}{cotx}=\frac{1}{{\displaystyle \frac{\cos x}{\sin x}}} \\ \Rightarrow \frac{1}{cotx}=\frac{\sin x}{\cos x} \end{gathered}$$

We know that $\frac{\sin x}{\cos x}=\tan x$

Hence, the required answer is $\frac{1}{cotx}=\tan x$