Algebra and Trigonometry 10th Edition

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

Chapter 6 - 6.2 - Right Triangle Trigonometry - 6.2 Exercises - Page 442: 50


The identity is verified. $\frac{tan~β+cot~β}{tan~β}=csc^2β$

Work Step by Step

Use: $\frac{1}{tan~β}=cot~β$ $1+cot^2β=csc^2β$ $\frac{tan~β+cot~β}{tan~β}=\frac{tan~β}{tan~β}+\frac{cot~β}{tan~β}=1+\frac{cot~β}{\frac{1}{cot~β}}=1+cot~β~\frac{cot~β}{1}=1+cot^2β=csc^2β$
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