Answer
$-\cos\theta$
Work Step by Step
Use the subtraction formula for cosine, $\cos (A-B)=\cos A\cos B+\sin A\sin B$:
$\cos(\theta-180^\circ)$
$=\cos\theta\cos 180^\circ+\sin\theta\sin 180^\circ$
$=\cos\theta*(-1)+\sin\theta*0$
$=-\cos\theta$