Answer
Verified below.
Work Step by Step
As we know that, $\cos \left( A+B \right)=\cos A\cos B-\sin A\sin B $.
Therefore:
$\cos \left( \theta +\frac{3\pi }{2} \right)$, can be written as:
$\begin{align}
& \cos \left( \theta +\frac{3\pi }{2} \right)=\cos \theta \cos \left( \frac{3\pi }{2} \right)-\sin \theta \sin \left( \frac{3\pi }{2} \right) \\
& =\cos \theta \left( 0 \right)-\sin \theta \left( -1 \right) \\
& =0+\sin \theta \\
& =\sin \theta
\end{align}$
Therefore, from (1) we get;
$\cos \left( \theta +\frac{3\pi }{2} \right)=\sin \theta $
