Precalculus (6th Edition) Blitzer

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

Chapter 5 - Section 5.1 - Verifying Trigonometric Identities - Exercise Set - Page 658: 9


See the explanation below.

Work Step by Step

To verify the given identity, ${{\cos }^{2}}x-{{\sin }^{2}}x=1-2{{\sin }^{2}}x$ Recall Trigonometric Identity, ${{\sin }^{2}}x+{{\cos }^{2}}x=1$ Use the above identity and solve the left side of the given expression, $\begin{align} & {{\cos }^{2}}x-{{\sin }^{2}}x=\left( 1-{{\sin }^{2}}x \right)-{{\sin }^{2}}x \\ & =1-2{{\sin }^{2}}x \end{align}$ Hence, it is proved that the given identity holds true.
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