Precalculus (6th Edition) Blitzer

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

Chapter 5 - Section 5.2 - Sum and Difference Formulas - Concept and Vocabulary Check - Page 668: 7


The required solution is False.

Work Step by Step

We have the identity $\cos \left( x+y \right)$ that is equal to the product of the cosine of the first angle and cosine of the second angle minus the product of the sine of the first angle and the second angle. It can be understood by way of an example. Let us say that cos x is $-\frac{5}{13}$ and cos y is $\frac{4}{5}$ and sin x is $\frac{12}{13}$ and sin y is $\frac{3}{5}$. Now, using the sum formula for cosine, we get: $\begin{align} & \cos \left( x+y \right)=\cos x\cos y-\sin x\sin y \\ & \cos \left( -\frac{5}{13}+\frac{4}{5} \right)=\left( -\frac{5}{13} \right)\left( \frac{4}{5} \right)-\left( \frac{12}{13} \right)\left( \frac{3}{5} \right) \\ & =-\frac{20}{65}-\frac{36}{65} \\ & =-\frac{56}{65} \end{align}$ Thus, the provided statement is False.
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