Precalculus (6th Edition)

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

Chapter 7 - Trigonometric Identities and Equations - 7.2 Verifying Trigonometric Identities - 7.2 Exercises: 54

Answer

$\frac{\sin^2\theta}{\cos\theta}=\sec\theta-\cos\theta$

Work Step by Step

Start with the right side: $\sec\theta-\cos\theta$ Write in terms of sine and cosine: $=\frac{1}{\cos\theta}-\cos\theta$ Get a common denominator: $=\frac{1}{\cos\theta}-\frac{\cos^2\theta}{\cos\theta}$ Simplify: $=\frac{1-\cos^2\theta}{\cos\theta}$ $=\frac{\sin^2\theta}{\cos\theta}$ Since this equals the left side, the identity has been proven.
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