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: 49


The identity is verified. $\frac{sin~θ}{cos~θ}+\frac{cos~θ}{sin~θ}=csc~θ~sec~θ$

Work Step by Step

Use: $\frac{1}{sin~θ}=csc~θ$ $\frac{1}{cos~θ}=sec~θ$ $sin^2θ+cos^2θ=1$ $\frac{sin~θ}{cos~θ}+\frac{cos~θ}{sin~θ}=\frac{sin~θ(sin~θ)}{cos~θ(sin~θ)}+\frac{cos~θ(cos~θ)}{sin~θ(cos~θ)}=\frac{sin^2θ}{sin~θ~cos~θ}+\frac{cos^2θ}{sin~θ~cos~θ}=\frac{sin^2θ+cos^2θ}{sin~θ~cos~θ}=\frac{1}{sin~θ~cos~θ}=\frac{1}{sin~θ}\frac{1}{cos~θ}=csc~θ~sec~θ$
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