Question

CosA+CosB-CosC = -1+4CosA/2. CosB/2.SinC/2

Answer 1

\[
\cos(A)+\cos(B)-\cos(C)=-1+4\cos\left(\frac{A}{2}\right)\cos\left(\frac{B}{2}\right)\sin\left(\frac{C}{2}\right)
\]
Is that the equation?

Answer 2

A+B+C=180
A=180-(B+C)
cos A=cos{180-(B+C)}=-cos(B+C)=\[-[1-2\sin ^2\frac{ B+C }{ 2 }]\]
\[=-1+2\sin ^2\frac{ B+C }{ 2 }\]
\[\cos2x=1-2\sin ^2x\]
\[\cos x-\cos y=-2\sin \frac{ x+y }{ 2 }\sin \frac{ x-y }{ 2 }\]
use it and complete it.