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: 17


The trigonometric Identity is verified. $sin~t~csc(\frac{\pi}{2}-t)=tan~t$

Work Step by Step

We know that: $csc(\frac{\pi}{2}-t)=sec~t~~$ (Cofunction Identity, page 508) $sec~t=\frac{1}{cos~t}$ Start at the left side of the equation: $sin~t~csc(\frac{\pi}{2}-t)=sin~t~sec~t=sin~t~\frac{1}{cos~t}=\frac{sin~t}{cos~t}=tan~t$
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