Chapter 7 - Section 7.2 - Addition and Subtraction Formulas - 7.2 Exercises - Page 551: 28

$\cos(x-\pi)=-\cos(x)$

$\cos(x-\pi)$ Expand using subtraction formula for cosine on page 545: $=\cos(x)\cos(\pi)+\sin(x)\sin(\pi)$ Evaluate $\cos(\pi)$ and $\sin(\pi)$: $=\cos(x)*(-1)+\sin(x)*0$ Simplify: $=-\cos(x)$ Therefore, $\cos(x-\pi)=-\cos(x)$.