a) Xét $\cos A + \cos B + \cos C + \cos \frac{\pi}{3}$
$= 2.\cos \frac{A+B}{2}.\cos \frac{A-B}{2} + 2. \cos (\frac{C}{2}+\frac{\pi}{6}).\cos(\frac{C}{2}-\frac{\pi}{6})$
$\leq 2.\cos \frac{A+B}{2}+2.\cos(\frac{C}{2}+\frac{\pi}{6})$
$\leq 4.cos(\frac{A+B+C}{4}+\frac{\pi}{12})=4.\cos(\frac{\pi}{4}+\frac{\pi}{12}) =2$
$\Rightarrow \cos A +\cos B+ \cos C \leq \frac{3}{2}$
c) xét tương tự