In a triangle ABC , A= B+ C then what is ( B 2 )+ ( B 2 ) equal to ?

Step-by-step solution

Given A = B + C Using the half-angle and sum-to-product formulas: 2 ( A 2 ) ( A 2 ) = 2 ( B+C 2 ) ( B-C 2 ) In ABC , A + B + C = , so B+C 2 = 2 - A 2 . This yields ( B+C 2 ) = ( A 2 ) . Substituting this into the equation: 2 ( A 2 ) ( A 2 ) = 2 ( A 2 ) ( B-C 2 ) Since A (0, ) , ( A 2 ) 0 . Dividing both sides by 2 ( A 2 ) : ( A 2 ) = ( B-C 2 ) Since both A 2 and B-C 2 lie in (- 2 , 2 ) , we have: A 2 = B-C 2 This implies either A = B - C or A = C - B . If A = B - C , then B = A + C . Since A + B + C = , we get 2B =