Question

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

Answer 1

Simplify the given expression

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

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

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

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

So we got $\frac{1}{\tan x}=cotx$

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