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MHT CET202526 Apr 2025Morning ShiftMathematicsProperties of TrianglesActual

In a triangle ABC , with usual notations, ( A+B 2 ) ( A-B 2 )=

Options

  1. Aa+b a-b
  2. Ba-b a+b
  3. Ca a+b
  4. Db a- b

Correct answer

B. a-b a+b

Step-by-step solution

In triangle ABC where A + B + C = , the expression ( A+B 2 ) ( A-B 2 ) simplifies as follows. Using the angle sum property, A+B 2 = - C 2 = 2 - C 2 . By the complementary angle identity ( 2 - x ) = x , we obtain: ( A+B 2 ) = ( C 2 ) . Napier's Analogy gives ( A-B 2 ) = a-b a+b ( C 2 ) . Since ( C 2 ) = 1 ( C 2 ) , this becomes: ( A-B 2 ) = a-b a+b 1 ( C 2 ) . Substituting both results into the original expression: ( C 2 ) ( a-b a+b 1 ( C 2 ) ) = a-b a+b . Thus, the simplified expression is a-b a+b .

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