Precalculus (6th Edition) Blitzer

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

Chapter 5 - Section 5.4 - Product-to-Sum and Sum-to-Product Formulas - Exercise Set - Page 691: 52


The given statement makes sense.

Work Step by Step

$\sin \alpha \cos \beta =\frac{1}{2}\left[ \sin \left( \alpha +\beta \right)+sin\left( \alpha -\beta \right) \right]$ is one of the product-to-sum formulas, which reflects that the product of a sine and a cosine is equal to the half of the sum of the two sines expression. Now, consider another product-to-sum formula, that is $\sin \alpha \sin \beta =\frac{1}{2}\left[ \cos \left( \alpha -\beta \right)-\cos \left( \alpha +\beta \right) \right]$. So, this formula reflects that the product of two sines is equal to half of the difference between the two cosines expression. Thus, both product-to-sum formulas appear to be similar. It creates confusion, and thus, it becomes difficult to memorize.
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