Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 7 - Section 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas - 7.3 Exercises - Page 561: 72



Work Step by Step

Use the third Sum-to-Product Formula, $\cos(x+y)=2\cos \frac{x+y}{2}\cos \frac{x-y}{2}$. $\cos\frac{\pi}{12}+\cos \frac{5\pi}{12}$ $=2\cos\frac{\frac{\pi}{12}+\frac{5\pi}{12}}{2}\cos\frac{\frac{\pi}{12}-\frac{5\pi}{12}}{2}$ $=2\cos \frac{\frac{\pi}{2}}{2}\cos\frac{-\frac{\pi}{3}}{2}$ $=2\cos \frac{\pi}{4}\cos(-\frac{\pi}{6})$ $=2\times\frac{\sqrt{2}}{2}\times\frac{\sqrt{3}}{2}$ $=\frac{\sqrt{6}}{2}$
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.