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:
$\text{LHS } =\cos(\pi + \theta)
\\=\cos (\pi) \cos (\theta) -\sin \pi \sin(\theta)
\\=(-1)( \cos(\theta)) -(0) (\sin(\theta))
\\=-\cos (\theta)\\=\text{ RHS}$
