Trigonometry (10th Edition)

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

Chapter 5 - Trigonometric Identities - Section 5.5 Double-Angle Identities - 5.5 Exercises - Page 231: 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, $$1-2\sin^215^\circ=\frac{\sqrt3}{2}$$
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