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 736: 9



Work Step by Step

$\displaystyle \frac{\sin^{2}\theta}{\cos^{2}\theta}(1+\frac{\cos^{2}\theta}{\sin^{2}\theta})=\frac{\sin^{2}\theta}{\cos^{2}\theta}+\frac{\sin^{2}\theta}{\cos^{2}\theta}\times\frac{\cos^{2}\theta}{\sin^{2}\theta}$ $=\displaystyle \frac{\sin^{2}\theta}{\cos^{2}\theta}+1$ $=\displaystyle \frac{\sin^{2}\theta+\cos^{2}\theta}{\cos^{2}\theta}$ $=\displaystyle \frac{1}{\cos^{2}\theta}$ $=(\displaystyle \frac{1}{\cos\theta})^{2}$ $=\sec^{2}\theta$
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