Answer
We write $$\cos195^\circ=\cos(180^\circ+15^\circ)$$
then apply the cosine sum identity to expand.
Finally, the result is $$\cos195^\circ=-\cos15^\circ$$
Work Step by Step
As required by the exercise, we write $195^\circ$ as the sum of $180^\circ$ and $15^\circ$.
$$195^\circ=180^\circ+15^\circ$$
That means $$\cos195^\circ=\cos(180^\circ+15^\circ)$$
Now we apply the cosine sum identitiy, which states
$$\cos(A+B)=\cos A\cos B-\sin A\sin B$$
Therefore, $$\cos195^\circ=\cos 180^\circ\cos15^\circ-\sin180^\circ\sin15^\circ$$
$$\cos195^\circ=-1\times\cos15^\circ-0\times\sin15^\circ$$ (as $\cos180^\circ=-1$ and $\sin180^\circ=0$)
$$\cos195^\circ=-\cos15^\circ$$
