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: 55

Answer

See below.

Work Step by Step

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