Chapter 14.5, Problem 38E

To determine

Simplify the term.

Answer to Problem 38E

  $x={\tan }^{-1}\frac{\pi }{4}$

Explanation of Solution

Given information:

Given: $\tan x+\cot x=2$

Calculation:

Here, we have to simplify $\tan x+\cot x=2$ :

  $\begin{array}{l}\cot x=\frac{1}{\tan x}\\ \tan x+\cot x-2=0\\ \tan x+\frac{1}{\tan x}-2=0\\ \frac{\tan {\left(x\right)}^2+1-2\tan x}{\tan x}=0\\ \tan {\left(x\right)}^2+1-2\tan x=0\\ {\left(\tan \left(x\right)-1\right)}^2=0\\ \tan \left(x\right)-1=0\\ \tan x=1\\ x={\tan }^{-1}1\\ x={\tan }^{-1}\frac{\pi }{4}\end{array}$

Hence, the required answer is $x={\tan }^{-1}\frac{\pi }{4}$ .