Answer
See the steps.
Work Step by Step
$\sin{(\dfrac{3\pi}{2}-x)} = \sin{\dfrac{3\pi}{2}} \cos{x} - \cos{\dfrac{3\pi}{2}} \sin{x}$
$\sin{(\dfrac{3\pi}{2}-x)} = -1 \times \cos{x} - 0 \times \sin{x} = - \cos{x}$
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 5.2 - Sum and Difference Formulas - 5.2 Problem Set - Page 288: 27
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