Answer
$ -\frac{\sqrt {2+\sqrt 3}}{2}$
Work Step by Step
$cos(165^\circ)=-\sqrt {\frac{1+cos(330^\circ)}{2}}=-\sqrt {\frac{1+\frac{\sqrt 3}{2}}{2}}=-\frac{\sqrt {2+\sqrt 3}}{2}$
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 - 7.6 Double-angle and Half-angle Formulas - 7.6 Assess Your Understanding - Page 497: 25
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