Chapter 14.2, Problem 41PPS

To determine

To find :Expression to either constant or a basic trigonometric function.

Answer to Problem 41PPS

  $\cos \theta$ is a basic trigonometric function.

Explanation of Solution

Given information :

We know that, $\frac{\tan \left(\frac{\pi }{2}-\theta \right)\mathrm{cosec}\theta }{{\mathrm{cosec}}^2\theta }$

Calculation :

  $\begin{array}{l}\frac{\tan \left(\frac{\pi }{2}-\theta \right)\mathrm{cosec}\theta }{{\mathrm{cosec}}^2\theta }\left\{\because \tan \left(\frac{\pi }{2}-\theta \right)=\cot \theta \right\}\\ =\frac{\cot \theta }{\mathrm{cosec}\theta }\\ =\frac{\cos \theta }{\sin \theta }\times \frac{\sin \theta }{1}\\ =\cos \theta \end{array}$