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 521: 56



Work Step by Step

Use $tan(\frac{\pi}{2}-u)=tan(90°-u)=cot~u$ and $cot(\frac{\pi}{2}-u)=cot(90°-u)=tan~u$ Also: $1+cot^2u=csc^2u$ $cot^2u-csc^2u=-1$ $1+tan^2u=sec^2u$ $tan^2u-sec^2u=-1$ $tan^263°+cot^216°-sec^274°-csc^227°=tan^2(90°-27°)+cot^2(90°-74°)-sec^274°-csc^227°=(cot^227°-csc^227°)+(tan^274°-sec^274°)=-1-1=-2$
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