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MHT CET202520 Apr 2025Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If A + B = 2 then the maximum value of A B is

Options

  1. A1 2
  2. B1 2
  3. C- 1 2
  4. D- 1 2

Correct answer

B. 1 2

Step-by-step solution

Given A + B = 2 , we have B = 2 - A . The expression A B becomes A ( 2 - A ) . Using the identity ( 2 - ) = , this simplifies to A A . Applying the double-angle identity (2A) = 2 A A , we write A A = 1 2 (2A) . The maximum value of (2A) is 1 , so the maximum value of the expression is 1 2 1 = 1 2 . The correct option is B .

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