Chapter 14.5, Problem 1E

To determine

To find : Simplification of $\frac{\cos \theta }{\cot \theta +\tan \theta }$ by writing it in terms of $\sin \theta$ .

Answer to Problem 1E

  $\sin \theta$

Explanation of Solution

Given information :

We know that, The given information is $\frac{\sec \theta }{\cot \theta +\tan \theta }$

Calculation :

The given equation is

  $\begin{array}{l}=\frac{\sec \theta }{\cot \theta +\tan \theta }\\ =\frac{\frac{1}{\cos \theta }}{\frac{\cos \theta }{\sin \theta }+\frac{\sin \theta }{\cos \theta }}\\ =\frac{\frac{1}{\cos \theta }}{\frac{{\cos }^2\theta +{\sin }^2\theta }{\sin \theta \cos \theta }}\\ =\sin \theta \end{array}$