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: 40



Work Step by Step

$$1-2\sin^222\frac{1^\circ}{2}$$ Just like the above exercises, recall that $$1-2\sin^2A=\cos2A$$ Therefore, replace $A=22\frac{1^\circ}{2}$, we can apply the above identity to $1-2\sin^222\frac{1^\circ}{2}$. $$1-2\sin^222\frac{1^\circ}{2}=\cos\Big(2\times22\frac{1^\circ}{2}\Big)$$ $$1-2\sin^222\frac{1^\circ}{2}=\cos45^\circ$$ $$1-2\sin^222\frac{1^\circ}{2}=\frac{\sqrt2}{2}$$
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