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: 35

Answer

See below.

Work Step by Step

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

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.