Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 5 - Section 5.3 - Double-Angle, Power-Reducing, and Half-Angle Formulas - Exercise Set - Page 683: 102

Answer

The statement makes sense.

Work Step by Step

The provided statement makes sense because consider the following sum of angle identities: $\begin{align} & \sin \left( x+y \right)=\sin x\cdot \cos y+\cos x\cdot \sin y \\ & \cos \left( x+y \right)=\cos x\cdot \cos y-\sin x\cdot \sin y \\ \end{align}$ If instead of adding $y\text{ to x}$, add $\text{x to x}$ i.e. replace $y\text{ by x}$: $\begin{align} & \sin \left( x+x \right)=\sin x\cdot \operatorname{cosx}+\cos x\cdot \operatorname{sinx} \\ & sin2x=2sinx\cdot cosx \\ & \cos \left( x+x \right)=\cos x\cdot \operatorname{cosx}-\sin x\cdot \operatorname{sinx} \\ & \cos 2x={{\cos }^{2}}x-{{\sin }^{2}}x \end{align}$ These are the double angle identities.
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