Answer
$\sqrt {\frac{1-x}{2}}$
Work Step by Step
Let $cos^{-1}x=y$, we have $cos(y)=x, $ and
$sin(\frac{1}{2}cos^{-1}x)=sin(\frac{y}{2})=\sqrt {\frac{1-cos(y)}{2}}=\sqrt {\frac{1-x}{2}}$
Precalculus: Mathematics for Calculus, 7th Edition
by Stewart, James; Redlin, Lothar; Watson, Saleem
Published by
Brooks Cole
ISBN 10:
1305071751
ISBN 13:
978-1-30507-175-9
Chapter 7 - Section 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas - 7.3 Exercises - Page 561: 45
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