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MHT CET202314 May 2023Morning ShiftMathematicsProperties of TrianglesActual

If the angles A , B and C of a triangle are in an Arithmetic Progression and if a , b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression a c 2 C + c a 2 ~A is

Options

  1. A1 2
  2. B3 2
  3. C1
  4. D3

Correct answer

D. 3

Step-by-step solution

A, B, C are in A.P. array ll & A+C=2 B & Also, A+B+C=180^ & B=60^ & B y sine rule, & A a = B b = C c =k & A=a k, B=b k, C=c k & a c 2 C+ c a 2 A & = a c (2 C C)+ c a (2 A A) & = a c (2 ck C)+ c a (2 a k A) & =2 k a C+2 k c A & =2 k(a C+c A) array array ll =2 ~kb & [ b= a C + c A ] =2 B & =2 3 2 & [ B =60^ ] = 3 & array

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