Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 5 - Trigonometric Identities - Section 5.3 Sum and Difference Identities for Cosine - 5.3 Exercises - Page 218: 9


$$\cos75^\circ=\frac{\sqrt 6-\sqrt 2}{4}$$

Work Step by Step

$$A=\cos75^\circ$$ We can rewrite $75^\circ$ into the sum of $30^\circ$ and $45^\circ$, which means $$A=\cos(30^\circ+45^\circ)$$ Now we apply the identity for cosine of a sum: $$A=\cos30^\circ\cos45^\circ-\sin30^\circ\sin45^\circ$$ $$A=\frac{\sqrt 3}{2}\frac{\sqrt 2}{2}-\frac{1}{2}\frac{\sqrt 2}{2}$$ $$A=\frac{\sqrt 6}{4}-\frac{\sqrt 2}{4}$$ $$A=\frac{\sqrt 6-\sqrt 2}{4}$$
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.