The value of (a + b + c)(cos A + cos B + cos C) is :

$\sum a\sin^2\frac{A}{2}$ $\sum a\cos^2\frac{A}{2}$ $2\sum a\sin^2\frac{A}{2}$ $2\sum a\cos^2\frac{A}{2}$

$2\sum a\cos^2\frac{A}{2}$

$\sum a\cos A+\sum (b\cos C+c\cos B)=a\cos A +b\cos B+c\cos C + (a+b+c)=\sum a(1+\cos A)=2\sum a\cos^2\frac{A}{2}$.