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: 48



Work Step by Step

$$X=\cos^22x-\sin^22x$$ Recall the Double-Angle Identity for cosine, which states $$\cos^2A-\sin^2A=\cos2A$$ Therefore, here we can absolutely apply the identity right away with $A=2x$, meaning that $$\cos^22x-\sin^22x=\cos(2\times2x)$$ $$\cos^22x-\sin^22x=\cos4x$$ Therefore, $$X=\cos4x$$ In conclusion, the result is $$\cos^22x-\sin^22x=\cos4x$$
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