Chapter 5 - Trigonometric Identities - Section 5.3 Sum and Difference Identities for Cosine - 5.3 Exercises - Page 219: 45

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

$$A=\cos(\theta-180^\circ)$$ According to the identity of cosine difference: $$\cos(A-B)=\cos A\cos B+\sin A\sin B$$ $A$ would be: $$A=\cos\theta\cos180^\circ+\sin\theta\sin180^\circ$$ $$A=\cos\theta\times(-1)+\sin\theta\times0$$ $$A=-\cos\theta$$