CCSS Honors 9.1 Example 3

Write a two-column proof of the trigonometric identity [math]\frac{1+\cos\theta}{\sin\theta} = \csc\theta+\cot\theta[/math].

[list=1] [*]Create the outline for the two-column proof. [*]Rewrite the expression [math]\frac{1+\cos\theta}{\sin\theta}[/math] as the sum of two fractions. [*]Use the reciprocal identity [math]\csc\theta=\frac{1}{\sin\theta}[/math] to simplify the expression [math]\frac{1}{\sin\theta}+\frac{\cos\theta}{\sin\theta}[/math]. [*]Use the ratio identity [math]\cot\theta=\frac{\cos\theta}{\sin\theta}[/math] to rewrite the expression [math]\csc\theta+\frac{\cos\theta}{\sin\theta}[/math]. [*]Fill in the columns of the two-column proof. [/list]