Algebra and Trigonometry 10th Edition

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

Chapter 7 - 7.1 - Using Fundamental Identities - 7.1 Exercises - Page 513: 39



Work Step by Step

We know that: $sin^2x+cos^2x=1$ $cos^2x=1-sin^2x$ $csc^2x=1+cot^2x$ $csc^2x-1=cot^2x$ $cot~x=\frac{cos~x}{sin~x}$ So: $\frac{1-sin^2x}{csc^2x-1}=\frac{cos^2x}{cot^2x}=\frac{cos^2x}{(\frac{cos~x}{sin~x})^2}=cos^2x~\frac{sin^2x}{cos^2x}=sin^2x$
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