In a $\Delta ABC,a({\cos }^{2}C+{\cos }^{2}B)+\cos A(c\cos C+b\cos B)=$

$\begin{array}{l}a({\cos }^{2}C+{\cos }^{2}B)+\cos A(c\cos C+b\cos B)\\ =a{\cos }^{2}C+a{\cos }^{2}B+c\cos C\cos A+b\cos A\cos B\\ =\cos C(a\cos C+c\cos A)+\cos B(a\cos B+b\cos A)\\ b\cos C+c\cos B=a\end{array}$