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 6.7 Product-to-Sum and Sum-to-Product Formulas - 6.7 Assess Your Understanding - Page 524: 33

Answer

See below.

Work Step by Step

Use the Sum-to-Product Formula, we have: $LHS=\frac{sin(4\theta)+sin(8\theta)}{cos(4\theta)+cos(8\theta)}=\frac{2sin(\frac{4\theta+8\theta}{2})cos(\frac{4\theta-8\theta}{2})}{2cos(\frac{4\theta+8\theta}{2})cos(\frac{4\theta-8\theta}{2})} =\frac{sin(6\theta)}{cos(6\theta)}=tan(6\theta)=RHS$
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