Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 7 - Analytic Trigonometry - 7.4 Trigonometric Identities - 7.4 Assess Your Understanding - Page 477: 90

Answer

See below.

Work Step by Step

We need to show $1+cos\theta+sin\theta=(1+cos\theta-sin\theta)(sec\theta+tan\theta)$. We have $RHS=sec\theta+tan\theta+cos\theta sec\theta+cos\theta tan\theta-sin\theta sec\theta-sin\theta tan\theta=sec\theta+tan\theta+1+sin\theta-tan\theta-sin\theta tan\theta=1+sec\theta+sin\theta-sin\theta tan\theta=1+sin\theta+\frac{1-sin^2\theta}{cos\theta}=1+sin\theta+cos\theta=LHS$
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