Precalculus (6th Edition) Blitzer

Published by Pearson

Chapter 10 - Cumulative Review Exercises - Page 1128: 46

Verified below.

Work Step by Step

We have $\frac{1-{{\tan }^{2}}x}{1+{{\tan }^{2}}x}=\cos 2x$ By evaluating the left side, \begin{align} & \text{Left side}=\frac{1-{{\tan }^{2}}x}{1+{{\tan }^{2}}x} \\ & =\frac{{{\cos }^{2}}x-{{\sin }^{2}}x}{{{\cos }^{2}}x+{{\sin }^{2}}x} \\ & =\frac{\cos 2x}{1} \\ & =\cos 2x \end{align} Therefore, $\text{left side = right side}$. Thus, we can say that the identity is true. Hence, verified.

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