Answer
See below.
Work Step by Step
$LHS=\frac{sec\theta-cos\theta}{sec\theta+cos\theta}=\frac{sec\theta-cos\theta}{sec\theta+cos\theta}\times\frac{cos\theta}{cos\theta}=\frac{1-cos^2\theta}{1+cos^2\theta}=\frac{sin^2\theta}{1+cos^2\theta}=RHS$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 6 - Analytic Trigonometry - Section 6.4 Trigonometric Identities - 6.4 Assess Your Understanding - Page 497: 64
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