Chapter 14.7, Problem 7WE

To determine

To Find: Thevalue of the given trigonometric equation.

Answer to Problem 7WE

The value of the expression is $\frac{3\pi }{4}$ .

Explanation of Solution

Given:

The given expression is ${\cot }^{-1}\left(\tan \left(\frac{3\pi }{4}\right)\right)$ .

Calculation:

Consider the given trigonometric expression is,

  ${\cot }^{-1}\left(\tan \left(\frac{3\pi }{4}\right)\right)$

Consider the above expression as,

  $\begin{array}{l}y={\cot }^{-1}\left(\tan \left(\frac{3\pi }{4}\right)\right)\\ \cot y=\left(\tan \left(\frac{3\pi }{4}\right)\right)\\ \cot y=-1\\ y={\cot }^{-1}\left(-1\right)\end{array}$

Solve further as,

  $\begin{array}{c}y=\mathrm{arccot}\left(-1\right)\\ =\frac{3\pi }{4}\end{array}$