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 520: 38

Answer

The identity is verified. $sec^6x(sec~x~tan~x)-sec^4x(sec~x~tan~x)=sec^5x~tan^3x$

Work Step by Step

$sec^6x(sec~x~tan~x)-sec^4x(sec~x~tan~x)=sec^2x~sec^4x(sec~x~tan~x)-sec^4x(sec~x~tan~x)=(sec^2x-1)sec^4x(sec~x~tan~x)=tan^2x~sec^5x~tan~x=sec^5x~tan^3x$
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