Answer
$-\frac{\sqrt 2+\sqrt 6}{4}$
Work Step by Step
$cos165^\circ=cos(120^\circ+45^\circ)=cos120^\circ cos45^\circ-sin120^\circ sin45^\circ=(-\frac{1}{2})(\frac{\sqrt 2}{2})-(\frac{\sqrt 3}{2})(\frac{\sqrt 2}{2})=-\frac{\sqrt 2+\sqrt 6}{4}$
Precalculus (10th Edition)
by Sullivan, Michael
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: 13
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