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Expert-verified Found in: Page 500 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # Express the product $\mathrm{sin}\left(4\theta \right)\mathrm{sin}\left(2\theta \right)$ as a sum containing only sines or only cosines.

$\mathrm{sin}\left(4\theta \right)\mathrm{sin}\left(2\theta \right)=\frac{\mathrm{cos}\left(2\theta \right)-\mathrm{cos}\left(6\theta \right)}{2}$

See the step by step solution

## Step 1. Given expression

$\mathrm{sin}\left(4\theta \right)\mathrm{sin}\left(2\theta \right)$

## Step 2. Rewriting the expression

$2\mathrm{sin}A\mathrm{sin}B=\mathrm{cos}\left(A-B\right)-\mathrm{cos}\left(A+B\right)\phantom{\rule{0ex}{0ex}}So,\phantom{\rule{0ex}{0ex}}\mathrm{sin}\left(4\theta \right)\mathrm{sin}\left(2\theta \right)=\frac{\mathrm{cos}\left(2\theta \right)-\mathrm{cos}\left(6\theta \right)}{2}$ ### Want to see more solutions like these? 