### Home > PC > Chapter 7 > Lesson 7.3.3 > Problem7-124

7-124.

A technique similar to rationalizing the denominator can be used to transform some rational trigonometric expressions to different forms. For example, multiply numerator and denominator of $\frac { \operatorname { sin } ( \theta ) } { 1 + \operatorname { cos } ( \theta ) }$ by $1 – \cos\left(θ\right)$ and rewrite the expression in terms of sine and cosine. Now rewrite the expression in terms of other trig functions.

$\frac{\sin(\theta)}{1+\cos(\theta)}\cdot \frac{1-\cos(\theta)}{1-\cos(\theta)}=\frac{\sin(\theta)(1-\cos(\theta)}{1-\cos^{2}(\theta)}$

Use a Fundamental Pythagorean Identity and substitute.