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: 58


$\csc A\sin 2A-\sec A=\cos 2A\sec A$

Work Step by Step

Start with the left side: $\csc A\sin 2A-\sec A$ Rewrite in terms of sine and cosine: $=\frac{1}{\sin A}*2\sin A\cos A-\frac{1}{\cos A}$ Simplify: $=2\cos A-\frac{1}{\cos A}$ $=\frac{2\cos^2 A}{\cos A}-\frac{1}{\cos A}$ $=\frac{2\cos^2 A-1}{\cos A}$ $=\frac{\cos 2A}{\cos A}$ $=\cos 2A\sec A$ Since this equals the right side, the identity has been proven.
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