Answer
See below.
Work Step by Step
$LHS=\frac{cos(v)}{1+sin(v)}+\frac{1+sin(v)}{cos(v)}=\frac{cos^2(v)+1+2sin(v)+sin^2(v)}{cos(v)(1+sin(v))}=\frac{2(1+sin(v))}{cos(v)(1+sin(v))}=\frac{2}{cos(v)}=2sec(v)=RHS$
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: 52
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