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MHT CET202522 Apr 2025Morning ShiftMathematicsProperties of TrianglesActual

In a triangle ABC with usual notations if, ( B - C 2 )=x ~A 2 , then x=

Options

  1. Ac-a c+a
  2. Ba-b a+b
  3. Cb-c b+c
  4. Da+b a-b

Correct answer

C. b-c b+c

Step-by-step solution

Using Napier's Analogy, the trigonometric identity for ( B-C 2 ) relates sides and angles as ( B-C 2 ) = b-c b+c A 2 . The given equation ( B-C 2 ) = x A 2 matches this form. Equating the expressions for ( B-C 2 ) yields x A 2 = b-c b+c A 2 . Since A 2 0 for any triangle angle A (0, ) , division gives x = b-c b+c . Final answer: C

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