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 236: 1


$$2\cos^215^\circ-1=\frac{\sqrt3}{2}$$ 1 is matched with C.

Work Step by Step

$$X=2\cos^215^\circ-1$$ Recall the double-angle identities: $$2\cos^2A-1=\cos2A$$ Here $X$ is like the form of $2\cos^2A-1$ with $A=15^\circ$. Therefore, $$X=2\cos^215^\circ-1=\cos(2\times15^\circ)$$ $$X=\cos30^\circ$$ $$X=\frac{\sqrt3}{2}$$ So, $$2\cos^215^\circ-1=\frac{\sqrt3}{2}$$ We pick C here.
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