#### Answer

Express $\cos(180^\circ-\theta)$ as a function of $\theta$ alone.
$$\cos(180^\circ-\theta)=-\cos\theta$$

#### Work Step by Step

$$\cos(180^\circ-\theta)$$
To be expressed as a function of $\theta$ alone, we need here the identity for difference of cosines:
$$\cos(A-B)=\cos A\cos B+\sin A\sin B$$
Apply it to $\cos(180^\circ-\theta)$, we have
$$\cos(180^\circ-\theta)=\cos180^\circ\cos\theta+\sin180^\circ\sin\theta$$
$$\cos(180^\circ-\theta)=(-1)\times\cos\theta+0\times\sin\theta$$
$$\cos(180^\circ-\theta)=-\cos\theta$$
This is the ultimate function we need to find.