Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 5 - Trigonometric Identities - Section 5.6 Half-Angle Identities - 5.6 Exercises - Page 237: 40

Answer

$$\pm\sqrt{\frac{1+\cos20\alpha}{2}}=\cos10\alpha$$

Work Step by Step

$$\pm\sqrt{\frac{1+\cos20\alpha}{2}}$$ Here we notice at the start of the expression, there is the sign $\pm$, which means we do not have to decide whether to take positive or negative square root. From the half-angle identity for cosines: $$\pm\sqrt{\frac{1+\cos A}{2}}=\cos\frac{A}{2}$$ We can apply the identity to the given expression with $A=20\alpha$. $$\pm\sqrt{\frac{1+\cos20\alpha}{2}}=\cos\frac{20\alpha}{2}$$ $$\pm\sqrt{\frac{1+\cos20\alpha}{2}}=\cos10\alpha$$
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.