CPM Homework Help : PC3 Problem 9-81

Add the fractions and simplify: $\frac { 1 } { 1 - \operatorname { sin } ( \theta ) } + \frac { 1 } { 1 + \operatorname { sin } ( \theta ) }$

Step 1:

Create a common denominator.

Step 2:

Combine the two fractions.

Step 3:

Simplify. Be sure to use the Fundamental Pythagorean Identity.

$\frac{1+\sin(\theta)}{(1-\sin(\theta))(1+\sin(\theta))}+\frac{1-\sin(\theta)}{(1-\sin(\theta))(1+\sin(\theta))}$

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