Question

in a triangle ABC,
a(b cos C -c cos B)=
a. a square
b. b square - c square
c. 0

note: this question is from properties of triangle and a,b,c represents sides of triangle and A,B,C represents angles in triangle

please don't give useless answers and don't forget to give your answers with steps

Answer 1

Looks like there is a typing error in the given question.  Plus sign in place of minus sign in the parentheses.

=>  LHS should be a * (b Cos C + c Cos B)  and not a*(b CosC - c Cos B)

In a triangle ΔABC we have the Cosine rule:  (see diagram)
     a = b Cos C + c Cos B, 
         as Cos B = BD/AB   and Cos C = CD / AC.   AB = c,  BC = a,  AC = b.
     
So LHS = a * (b Cos C + c Cos B)
              = a * a 
              = a² 

=====
Alternately if there is no typing error then the working steps are:

  LHS = a ( b Cos C - c Cos B)
          = (b Cos C + c Cos B) (b Cos C - c Cos B)
          = b² Cos² C - c² Cos² B