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: 40


The identity is verified. $\frac{tan~x+tan~y}{1-tan~x~tan~y}=\frac{cot~x+cot~y}{cot~x~cot~y-1}$

Work Step by Step

Remember: $tan~x=\frac{1}{cot~x}$ $tan~x~cot~x=1$ $\frac{tan~x+tan~y}{1-tan~x~tan~y}=\frac{tan~x+tan~y}{1-tan~x~tan~y}~\frac{cot~x~cot~y}{cot~x~cot~y}=\frac{(tan~x~cot~x)~cot~y+cot~x~(tan~y~cot~y)}{cot~x~cot~y-(tan~x~cot~x)(tan~y~cot~y)}=\frac{cot~y+cot~x}{cot~x~cot~y-1}$
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