Áp dụng định lí côsin, ta có :
$\frac{cosA}{a}$ = $\frac{b2 + c2 - a2}{2abc}$;
$\frac{cosB}{b}$ = $\frac{a2 + c2 - b2}{2abc}$;
$\frac{cosC}{c}$ = $\frac{a2 + b2 - c2}{2abc}$.
=> $\frac{cosA}{a}$ + $\frac{cosB}{b}$ + $\frac{cosC}{c}$ = $\frac{a2 + b2 + c2}{2abc}$ .