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MHT CET202526 Apr 2025Evening ShiftMathematicsProperties of TrianglesActual

If the angles A, B and C of a triangle are in A.P. and if a, b and c denote the length of the sides opposite to A, B and C respectively, then the value of a b 2 B+ b a 2 A is

Options

  1. A3
  2. B3 2
  3. C1 3
  4. D1 2

Correct answer

A. 3

Step-by-step solution

Given that angles A , B , and C of a triangle are in arithmetic progression, and A + B + C = 180^ . Since A , B , C form an AP, 2B = A + C . Substituting yields 2B + B = 180^ , so 3B = 180^ and B = 60^ . Evaluate E = a b 2B + b a 2A . By the Sine Rule, a A = b B , so a b = A B and b a = B A . Thus E = ( A B ) 2B + ( B A ) 2A . Apply 2x = 2 x x : E = ( A B )(2 B B) + ( B A )(2 A A) . Simplify to E = 2 A B + 2 B A = 2( A B + A B) . Recognize the sine sum identity: E = 2 (A + B) = 2 (180^ - C) = 2 C . Since B = 60^ an

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