Chapter 14.5, Problem 6E

To determine

To calculate:The given equation ${\left(\cot \theta +1\right)}^2-2\cot \theta$

Answer to Problem 6E

  $\cos e{c}^2\theta$

Explanation of Solution

Given Information: An Expression ${\left(\cot \theta +1\right)}^2-2\cot \theta$ is given which is to be simplified.

Formula used: ${\cot }^2\theta =\cos e{c}^2\theta -1$

Calculation:

  $\begin{array}{l}GivenEquationis\\ {\left(\cot \theta +1\right)}^2-2\cot \theta \\ ={\cot }^2\theta +1+2\cot \theta -2\cot \theta \\ =\cos e{c}^2\theta -1+1\\ =\cos e{c}^2\theta \end{array}$