Question

a(cosC - cosB) = 2(b-c)cos^2(A\2)
Prove that LHS = RHS

Answer 1

I think you have doubts from that perimeter part onwards.
Here 2s is the perimeter of triangle.
No other thing about perimeter is to ne known to solve this.
Just 2s= a+b+c is enough.

The remaining part has added nothing new, just the simple trigonometry.

Hope you get it.
Simple explanation.just read again.