Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 14 - Trigonometric Identities and Equations - 14-1 Trigonometric Identities - Lesson Check: 1

Answer

$sec\theta=sec\theta$

Work Step by Step

Step 1: Replace $tan\theta$ with $\frac{sin\theta}{cos\theta}$ and replace $csc\theta$ with $\frac{1}{sin\theta}$ Step 2: Therefore $tan\theta\times$$csc\theta$= $\frac{sin\theta}{cos\theta}$$\times$$\frac{1}{sin\theta}$ Step 3: Canceling $sin\theta$ gives $tan\theta\times$$csc\theta$= $\frac{1}{cos\theta}$ Step 4: By definition, $\frac{1}{cos\theta}$= $sec\theta$ Hence, $tan\theta\times$$csc\theta$=$sec\theta$
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