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: 35


The identity is verified. $\frac{cot~x}{sec~x}=csc~x-sin~x$

Work Step by Step

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