In a triangle ABC , if a -2 ~b + c =0 , then ( A 2 ) ( C 2 )=

Step-by-step solution

We are given that a-2 b+c=0 2 b=a+c b = a + c 2 Now ( A 2 ) ( c 2 )= [ ( A 2 ) ( A 2 ) ] [ ( c 2 ) ( c 2 ) ] ( A 2 ) ( c 2 )= [ 2 ( A 2 ) ( A 2 ) 2 ^2 ( A 2 ) ] [ 2 ^2 ( c 2 ) 2 ( c 2 ) WS ( c 2 ) ] aligned & ( A 2 ) ( c 2 )= [ A 1- A ] 1+ c ( c) & ( A 2 ) ( c 2 )= ( k A k C ) [ 1+ c 1- A ] aligned array l By Sin ce rule a A = b Sin B = c Sin C = k array ( A 2 ) ( c 2 )= ( a c ) 1+ [ a ^2+ b ^2- c ^2 2 ab ] 1- [ b ^2+ c ^2- a ^2 2 bc ] aligned & ( A 2 ) ( c 2 )= ( a c ) [ (2 a b+a^2+b^2-c^2 ) 2 b c 2 a b (2 b c-b^2