Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix D - Trigonometry - D Exercises - Page A33: 58



Work Step by Step

Need to prove the identity $cos3\theta=4cos^{3}\theta-3cos\theta$ Now, $cos3\theta$ can be written as: $cos3\theta=cos(2\theta+\theta)$ Use sum identity for cosine. $cos 3\theta=cos(2\theta+\theta)=cos2\theta cos\theta-sin2\theta sin\theta$ $=(2cos^{2}\theta -1)cos\theta-(2sin\theta cos\theta ) sin\theta$ $=2cos^{3}\theta - cos\theta-2sin^{2}\theta cos\theta$ $=2cos^{3}\theta - cos\theta-2(1-cos^{2}\theta) cos\theta$ $=2cos^{3}\theta - cos\theta-2 cos\theta+2cos^{3}\theta $ Hence, $cos3\theta=4cos^{3}\theta-3cos\theta$
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.