Question

IfA+B+C=180°than prove that cosA+cosB-cosC=4cosA/2.sinB/2.cisC/2

Answer 1

use your sum-to product formulas.

cosA + cosB = 2 cos(A+B)/2 cos(A-B)/2
A+B = 180-C so cos(A+B)/2 = cos(90 - C/2) = sin C/2
and now you see how to finish it off.