Answer
See proof below.
Work Step by Step
Apply the difference 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:
$\text{LHS } =\cos(\pi - \theta)
\\=\cos (\pi) \cos (\theta) +\sin \pi \sin(\theta)
\\=(-1)( \cos(\theta)) +(0) (\sin(\theta))
\\=-\cos (\theta)\\=\text{ RHS}$