Answer
$-\frac{\sqrt 3}{2}$
Work Step by Step
Using the Double Angle Formula in reverse,
$cos^2\theta - sin^2\theta =cos2\theta$
we have
$cos^275^\circ - sin^275^\circ =cos2(75^\circ)=cos150^\circ=-\frac{\sqrt 3}{2}$
Precalculus (6th Edition) Blitzer
by Blitzer, Robert F.
Published by
Pearson
ISBN 10:
0-13446-914-3
ISBN 13:
978-0-13446-914-0
Chapter 5 - Section 5.3 - Double-Angle, Power-Reducing, and Half-Angle Formulas - Exercise Set - Page 680: 17
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