Answer
$\frac{\sqrt 2}{2}$.
Work Step by Step
Recall the identity:
$$\sin 2x=2\sin x \cos x$$
We apply this identity to the given equation:
$$
2 \sin 22.5 \cos 22.5=
\sin2(22.5)=\sin45=\frac{\sqrt 2}{2}$$
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: 16
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