Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - Chapter 7 Test Prep - Review Exercises - Page 737: 53

Answer

$2\cos A-\sec A=\cos A-\frac{\tan A}{\csc A}$

Work Step by Step

Simplify the left side: $2\cos A-\sec A$ $=2\cos A-\frac{1}{\cos A}$ $=\frac{2\cos^2 A}{\cos A}-\frac{1}{\cos A}$ $=\frac{2\cos^2 A-1}{\cos A}$ $=\frac{\cos 2A}{\cos A}$ Simplify the right side: $\cos A-\frac{\tan A}{\csc A}$ $=\cos A-\frac{\frac{\sin A}{\cos A}}{\frac{1}{\sin A}}$ $=\cos A-\frac{\sin^2 A}{\cos A}$ $=\frac{\cos^2 A}{\cos A}-\frac{\sin^2 A}{\cos A}$ $=\frac{\cos^2 A-\sin^2 A}{\cos A}$ $=\frac{\cos 2A}{\cos A}$ Since both the left side and the right side are equal to $\frac{\cos 2A}{\cos A}$, they are equal to each other, and the identity is proven.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.