#### Answer

$$\cos(180^\circ+\theta)=-\cos\theta$$

#### Work Step by Step

$$A=\cos(180^\circ+\theta)$$
The strategy is to apply the cosine sum identity:
$$\cos(A+B)=\cos A\cos B-\sin A\sin B$$
That turns $A$ into
$$A=\cos180^\circ\cos\theta-\sin180^\circ\sin\theta$$
We have $\cos180^\circ=-\cos0^\circ=-1$ and $\sin180^\circ=\sin0^\circ=0$
$$A=-1\times\cos\theta-0\times\sin\theta$$
$$A=-\cos\theta$$