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: 18


The trigonometric Identity is verified. $sec^2y-cot^2(\frac{\pi}{2}-y)=1$

Work Step by Step

We know that: $cot(\frac{\pi}{2}-y)=tan~y~~$ (Cofunction Identity, page 508) $sec^2~y=1+tan^2y~~$ (Pythagorean Identity) Start at the left side of the equation: $sec^2y-cot^2(\frac{\pi}{2}-y)=1+tan^2y-(tan~y)^2=1+tan^2y-tan^2~y=1$
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