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: 37



Work Step by Step

We know that: $tan~β=\frac{sin~β}{cos~β}$ $\frac{1}{cos~β}=sec~β$ $sin^2β+cos^2β=1$ So: $sin~β~tan~β+cos~β=sin~β~\frac{sin~β}{cos~β}+cos~β=\frac{sin^2β}{cos~β}+cos~β=\frac{sin^2β}{cos~β}+\frac{cos~β(cos~β)}{cos~β}=\frac{sin^2β}{cos~β}+\frac{cos^2~β}{cos~β}=\frac{sin^2β+cos^2~β}{cos~β}=\frac{1}{cos~β}=sec~β$
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