Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 7 - 7.2 - Verifying Trigonometric Identities - 7.2 Exercises - Page 521: 52


Identity is verified. $tan^2x~sec^4x=(tan^2x+tan^4x)sec^2$

Work Step by Step

We know that: $1+tan^2x=sec^2x$ Start at the right side of the equation: $(tan^2x+tan^4x)sec^2=[tan^2x(1+tan^2x)]sec^2x=[tan^2x(sec^2x)]sec^2x=tan^2x(sec^2x·sec^2x)=tan^2x~sec^4x$
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