NDA Mathematics Question (2026) — Solution

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 = B = 2 . If A = C - B, then C = A + B. Since A + B + C = , we get 2C = C = 2 . Simplifying the required expression: ( B 2 ) + ( B 2 ) = ( B 2 ) ( B 2 ) + ( B 2 ) ( B 2 ) = ^2 ( B 2 ) + ^2 ( B 2 ) ( B 2 ) ( B 2 ) = 2 B If B = 2 , the value is 2 ( 2 ) = 2. If C = 2 , then B (0, 2 ), which means B 2. Since the given options are constants and the minimum possible value is 2, the only valid choice among the options is 2. Answer: 2