Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 7 - Analytic Trigonometry - 7.5 Sum and Difference Formulas - 7.5 Assess Your Understanding - Page 487: 25

Answer

$\dfrac{1}{2}$

Work Step by Step

Note that $\sin(\alpha+\beta)=\sin(\alpha)\cos(\beta)+\cos(\alpha)\sin(\beta)$. Hence, $\sin(20^\circ)\cos(10^\circ)+\cos(10^\circ)\sin(20^\circ)\\ =\sin(20^\circ+10^\circ)\\ =\sin(30^\circ)\\ =\frac{1}{2}$
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