Chapter 14.7, Problem 4WE

To determine

To find: The value of each given expression.

Answer to Problem 4WE

The value of given expression is $\frac{\pi }{4}$ .

Explanation of Solution

Given:

The given expression is as:

  ${\sec }^{-1}\left(\sec \left(-\frac{\pi }{4}\right)\right)$ .

The calculation is given as:

  $\begin{array}{c}\text{Let}{\sec }^{-1}\left(\sec \left(-\frac{\pi }{4}\right)\right)=x\text{where,}\left\{0\le x\le \pi ,x\ne \frac{\pi }{2}\right\}\\ \sec x=\sec \left(-\frac{\pi }{4}\right)\\ =\sec \left(\frac{\pi }{4}\right)\left[\because \sec \left(-x\right)=\sec x\right]\\ x=\frac{\pi }{4}\end{array}$

Therefore the value of given expression is $\frac{\pi }{4}$ .