Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

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: 77

Answer

See below.

Work Step by Step

$LHS=\frac{sec\theta}{1-sin\theta}=\frac{sec\theta}{1-sin\theta}\times\frac{1+sin\theta}{1+sin\theta}=\frac{sec\theta+sec\theta sin\theta}{1-sin^2\theta}=\frac{sec\theta+sec\theta sin\theta}{cos^2\theta}\times\frac{cos\theta}{cos\theta}=\frac{1+sin\theta}{cos^3\theta}=RHS$
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