18. In $\triangle A B C$, the three sides $a$, $b$, $c$ satisfy $2 b=a+c$. Find the value of $5 \cos A-4 \cos A \cos C+5 \cos C$.
$\begin{array}{l}\text { 18. } 2 b=a+c \Leftrightarrow 2 \sin B=\sin A+\sin C \Leftrightarrow 2 \cos \frac{A+C}{2}=\cos \frac{A-C}{2} \Leftrightarrow \tan \frac{A}{2} \tan \frac{C}{2}=\frac{1}{2} \Leftrightarrow \sqrt{\frac{1-\cos A}{1+\cos A}} \\ \cdot \sqrt{\frac{1-\cos C}{1+\cos C}}=\frac{1}{3} \Leftrightarrow 5 \cos A-4 \cos A \cos C+5 \cos C=4\end{array}$