Chapter 14.7, Problem 9WE

To determine

To Find: The value of the given trigonometric equation.

Answer to Problem 9WE

The value of the expression is $\frac{1}{2}$ .

Explanation of Solution

Given:

The given expression is $\tan \left({\cot }^{-1}2\right)$ .

Calculation:

Consider the given trigonometric expression is,

  $\tan \left({\cot }^{-1}2\right)$

Consider for $\frac{-\pi }{2}\le y\le \frac{\pi }{2}$ the value of ${\cot }^{-1}2={\tan }^{-1}\frac{1}{2}$ then,

  $\begin{array}{l}\frac{1}{x}=3\\ x=\frac{1}{3}<1\end{array}$

Then, the given expression is,

  $\begin{array}{c}\tan \left({\cot }^{-1}2\right)=\tan \left({\tan }^{-1}\frac{1}{2}\right)\\ =\frac{1}{2}\end{array}$