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 5.5 Double-Angle Identities - 5.5 Exercises - Page 237: 39

Answer

$$1-2\sin^215^\circ=\frac{\sqrt3}{2}$$

Work Step by Step

$$X=1-2\sin^215^\circ$$ - From Double-Angle Identity for cosine: $$\cos2A=1-2\sin^2A$$ So if we replace the above identity with $A=15^\circ$ as in $X$, we get $$X=\cos(2\times15^\circ)$$ $$X=\cos30^\circ$$ $$X=\frac{\sqrt3}{2}$$ Therefore, $$1-2\sin^215^\circ=\frac{\sqrt3}{2}$$
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.