Chapter 13, Problem 9CT

To determine

To find: The trigonometric function is prove.

Answer to Problem 9CT

The prove that $\cos \theta -\cot \theta \cos \theta =\sin \theta$ .

Explanation of Solution

Given information:

The given function is $\cos \theta -\cot \theta \cos \theta =\sin \theta$ .

Calculation:

Calculate the function

  $\begin{array}{l}\frac{1}{\sin \theta }-\frac{\cos \theta }{\sin \theta }\cos \theta =\frac{1-{\cos }^2\theta }{\sin \theta }\\ \frac{1-{\cos }^2\theta }{\sin \theta }=\frac{{\sin }^2\theta }{\begin{array}{c}\sin \theta \\ =\sin \theta \end{array}}\end{array}$

Therefore the prove that $\cos \theta -\cot \theta \cos \theta =\sin \theta$ .