Chapter 14.7, Problem 20WE

To determine

To Find: The simplified expression for the given expression without the use of trigonometric or inverse trigonometric functions.

Answer to Problem 20WE

The required expression is $\frac{1}{x}$ .

Explanation of Solution

Given:

The given expression is $\cot \left({\tan }^{-1}x\right)$ .

Calculation:

Consider the given expression is,

  $\cot \left({\tan }^{-1}x\right)$

Consider $y={\tan }^{-1}x$ , then,

  $\begin{array}{l}y={\tan }^{-1}x\\ x=\tan y\end{array}$

Then, the given equation is,

  $\cot \left(y\right)=\frac{1}{\tan y}$

Substitute $y={\tan }^{-1}x$ in the above equation as,

  $\cot \left(y\right)=\frac{1}{x}$