If $A+B+C=\pi$ then ${\cos }^{2}A+{\cos }^{2}B-{\cos }^{2}C$ equal to :

$\begin{array}{l}{\cos }^{2}A+{\cos }^{2}B-{\cos }^{2}C\\ ={\cos }^{2}A+\left(1-{\sin }^{2}B\right)-{\cos }^{2}C\\ =1+\left[{\cos }^{2}A-{\sin }^{2}B\right]-{\cos }^{2}C\\ =1+\cos (A+B)\cos (A-B)-{\cos }^{2}C\\ =1+\cos (\pi -C)\cos (A-B)-{\cos }^{2}C\\ =1-\cos C[\cos (A-B)+\cos C]\\ =1-\cos C[\cos (A-B)+\cos \{\pi -(A+B)\left\}\right]\\ =1-\cos C[\cos (A-B)-\cos (A+B\left)\right]\\ =1-\cos C[2\sin A\sin B]=1-2\sin A\sin B\cos C.\end{array}$