Answer
$-\frac{\sqrt3}{2}$
Work Step by Step
We know that $2\cos^2\theta-1=\cos(2\theta)$, hence here $2\cos^2(105^\circ)-1=\cos(210^\circ)=-\frac{\sqrt3}{2}$
Trigonometry 7th Edition
by McKeague, Charles P.; Turner, Mark D.
Published by
Cengage Learning
ISBN 10:
1111826854
ISBN 13:
978-1-11182-685-7
Chapter 5 - Section 5.3 - Double-Angle Formulas - 5.3 Problem Set - Page 297: 38
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