## Algebra 2 (1st Edition)

Published by McDougal Littell

# Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.3 Verify Trigonometric Identities - 14.3 Exercises - Skill Practice - Page 928: 33

See below.

#### Work Step by Step

Using the given identities: $\frac{1+\cos x}{\sin x }+\frac{\sin x}{1+\cos x}=\frac{(1+\cos x)^2+\sin^2 x}{\sin x(1+\cos x)}=\frac{1+2\cos x+\cos^2 x+\sin^2 x}{\sin x(1+\cos x)}=\frac{1+2\cos x+1}{\sin x(1+\cos x)}=\frac{2+2\cos x}{\sin x(1+\cos x)}=\frac{2(1+\cos x)}{\sin x(1+\cos x)}=\frac{2}{\sin x}=2\csc x$ Hence we showed what we had to.

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