Precalculus (10th Edition)

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

Chapter 8 - Applications of Trigonometric Functions - 8.1 Right Triangle Trigonometry; Applications - 8.1 Assess Your Understanding - Page 519: 27

Answer

$1$

Work Step by Step

Recall: (1) $\cos{(90^\circ-\theta)}=\sin{\theta}$ (2) $\sin{(90^\circ-\theta)}=\cos{\theta}$. (3) $\cos^2{\theta}+\sin^2{\theta}=1$ Thus, $\cos{35^\circ}\sin{55^\circ}+\sin{35^\circ}\cos{55^\circ}\\ =\cos{35^\circ}\cos{(90^\circ-55^\circ)}+\sin{35^\circ}\sin{(90^\circ-55^\circ)}\\ =\cos{35^\circ}\cos{35^\circ}+\sin{35^\circ}\sin{35^\circ}\\ =\cos^2{35^\circ}+\sin^2{35^\circ}\\ =1$
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