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MHT CET202523 Apr 2025Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If A + B =x and A + B = y , then ( A + B )=

Options

  1. A2 x y x^2+y^2
  2. Bx y x^2+y^2
  3. C2 x y y^2-x^2
  4. Dx y y^2-x^2

Correct answer

A. 2 x y x^2+y^2

Step-by-step solution

Given: A + B = x and A + B = y . Apply sum-to-product identities: A + B = 2 ( A+B 2 ) ( A-B 2 ) = x A + B = 2 ( A+B 2 ) ( A-B 2 ) = y Dividing these equations (assuming ( A-B 2 ) eq 0 ): ( A+B 2 ) = x y Using the tangent half-angle identity for sine: (A+B) = 2 ( A+B 2 ) 1 + ^2 ( A+B 2 ) = 2(x/y) 1 + (x/y)^2 Simplify: (A+B) = 2x/y (x^2 + y^2)/y^2 = 2x y y^2 x^2 + y^2 = 2xy x^2 + y^2 Result: 2xy x^2+y^2

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