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: 23

Answer

See below.

Work Step by Step

$LHS=cos(\theta)(tan(\theta)+cot(\theta))=cos(\theta)(\frac{sin(\theta)}{cos(\theta)}+\frac{cos(\theta)}{sin(\theta)})=cos(\theta)(\frac{sin^2(\theta)+cos^2(\theta)}{sin(\theta)cos(\theta)})=\frac{1}{sin(\theta)}=csc(\theta)=RHS$
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