Answer
See proof below.
Work Step by Step
Apply the sum formula:
$\cos(A+B)=\cos(A)\cos(B) -\sin(A)\sin(B)$
In order to prove the given identity, we simplify the left hand side $\text{LHS}$ as follows:
$\text{LHS } =\cos(\dfrac{\pi}{2}+\theta)
\\=\cos(\dfrac{\pi}{2})\cos(\theta) -\sin(\dfrac{\pi}{2})\sin(\theta)
\\=(0)( \cos(\theta)) -(1) (\sin(\theta))
\\=-\sin (\theta)\\=\text{ RHS}$