Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.3 Verify Trigonometric Identities - 14.3 Exercises - Skill Practice - Page 928: 20


$-\sec x$

Work Step by Step

Using the given identities: $\frac{\csc^2x-\cot^2x}{\sin(-x)\cot x}=\frac{\frac{1}{\sin^2x}-\frac{\cos^2x}{\sin^2x}}{-\sin x\frac{\cos x}{\sin x}}=\frac{\frac{1-\cos^2x}{\sin^2x}}{-\cos x}=\frac{\frac{\sin^2x}{\sin^2x}}{-\cos x}=\frac{1}{-\cos x}=-\sec x$
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