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AP EAMCET202318 May 2023Evening ShiftMathematicsProperties of TrianglesActual

In ABC , if ( A + B )( A - B )= C ( B + C ), then A=

Options

  1. A60^
  2. B30^
  3. C150^
  4. D120^

Correct answer

D. 120^

Step-by-step solution

Sine rule is A a = B b = C c =k Then A = ak , B = bk , C = ck aligned & Now, ( A+ B)( A- B)= C( B+ C) & (a k+b k)(a k-b k)=k c(k b+k c) & a^2-b^2=b c+c^2 a^2-b^2-c^2=b c & a^2-b^2-c^2 2 b c = 1 2 b^2+c^2-a^2 2 b c =- 1 2 & A=- 1 2 = 2 3 A= 2 3 =120^ aligned

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