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: 33


The identity is verified. $sec~x-cos~x=sin~x~tan~x$

Work Step by Step

$sin^2x+cos^2x=1$ $sin^2x=1-cos^2x$ $sec~x-cos~x=\frac{1}{cos~x}-cos~x~\frac{cos~x}{cos~x}=\frac{1}{cos~x}-\frac{cos^2x}{cos~x}=\frac{1-cos^2x}{cos~x}=\frac{sin^2x}{cos~x}=sin~x~\frac{sin~x}{cos~x}=sin~x~tan~x$
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