In a triangle ABC ,angle A=1/2angle B. If the sides opposite angle A,B and C are denoted by a, b and c resp., then which of the following relation is true? Ans) b^2-a^2=ac

From cosine formula, we know that
a^2 = b^2 + c^2 - 2cosB
Similarly, we know that
b^2  = a^2 + c^2 - 2cos2B
and
c^2 = b^2 + a^2 - 2cos(180 - 3B) 
Solving these 3 equations, we can get the desired equation.
Hope that helps.