Answer
See the steps.
Work Step by Step
$\cos{(x-\dfrac{3\pi}{2})} = \cos{x} \cos{\dfrac{3\pi}{2}} + \sin{x} \sin{\dfrac{3\pi}{2}}$
$\cos{(x-\dfrac{3\pi}{2})} = \cos{x} \times 0 + \sin{x} \times -1 = -\sin{x}$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.