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 5.4 Sum and Difference Identities for Sine and Tangent - 5.4 Exercises - Page 227: 36



Work Step by Step

$$X=\cos(45^\circ-\theta)$$ To expand the formula, cosine difference identity would be used: $$\cos(A-B)=\cos A\cos B+\sin A\sin B$$ That means $$X=\cos45^\circ\cos\theta+\sin45^\circ\sin\theta$$ $$X=\frac{\sqrt2}{2}\cos\theta+\frac{\sqrt2}{2}\sin\theta$$ $$X=\frac{\sqrt2\cos\theta+\sqrt2\sin\theta}{2}$$ $$X=\frac{\sqrt2(\cos\theta+\sin\theta)}{2}$$ Therefore, $$\cos(45^\circ-\theta)=\frac{\sqrt2(\cos\theta+\sin\theta)}{2}$$
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.