Question

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

Answer 1

Determine the simplified form of the expression $\frac{\mathbf{1}}{\mathbf{tan}\mathbf{x}}$:

It is known that $\tan x=\frac{\sin x}{\cos x}$ and $\tan x=\frac{1}{\cot x}$.

Case 1:

$\begin{array}{rcl}\frac{1}{\tan x}& =& \frac{1}{{\displaystyle \frac{\sin x}{\cos x}}}\\ & =& \frac{\cos x}{\sin x}\end{array}$

Case 2:

$\begin{array}{rcl}\frac{1}{\tan x}& =& \frac{1}{{\displaystyle \frac{1}{\cot x}}}\\ & =& \cot x\end{array}$

Hence, the simplified form of the expression $\frac{\mathbf{1}}{\mathbf{tan}\mathbf{x}}$ is $\frac{\mathbf{cos}\mathbf{x}}{\mathbf{sin}\mathbf{x}}$ or $\mathbf{cot}\mathit{x}$.