Answer
Please refer to the step-by-step part below.
Work Step by Step
Recalll:
(1) $\sin{(\alpha+\beta)}=\sin{(\alpha)}\cos{(\beta)}+\cos{(\alpha)}\sin{(\beta)}$
(2) $\sin{\frac{3\pi}{2}}=-1$ and $\cos{\frac{3\pi}{2}}=0$
Hence,
$\sin{(\frac{3\pi}{2}+\theta)}\\
=\sin{(\frac{3\pi}{2})}\cos{(\theta)}+\cos{(3\frac{\pi}{2}})\sin{(\theta)}\\=-1\cos{(\theta)}+0\cdot \sin{(\theta)}\\=-\cos{(\theta)}$
