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: 27

Answer

The identity is verified. See the graphs of $f(θ)=\frac{tan^2θ}{sec~θ}$ (Black) and $g(θ)=sin~θ~tan~θ$ (Red)
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Work Step by Step

$\frac{tan^2θ}{sec~θ}=tan^2θ·\frac{1}{sec~θ}=\frac{sin^2θ}{cos^2θ}·cos~θ=\frac{sin^2θ}{cos~θ}=sin~θ·\frac{sin~θ}{cos^2θ}=sin~θ~tan~θ$
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