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COMEDK20269 May 2026Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If A + 2A = x and A + 2A = y then the value of the expression (x^2 + y^2)(x^2 + y^2 - 3) equals

Options

  1. A3y
  2. B2y
  3. Cy 2
  4. D0

Correct answer

B. 2y

Step-by-step solution

Given equations are: x = A + 2A y = A + 2A Squaring and adding both equations, we get: x^2 + y^2 = ( A + 2A)^2 + ( A + 2A)^2 x^2 + y^2 = ( ^2 A + ^2 A) + ( ^2 2A + ^2 2A) + 2( A 2A + A 2A) Using the identity (P - Q) = P Q + P Q , we have: x^2 + y^2 = 1 + 1 + 2 (2A - A) x^2 + y^2 = 2 + 2 A Now, substituting this value into the given expression (x^2 + y^2)(x^2 + y^2 - 3) : (2 + 2 A)(2 + 2 A - 3) = (2 + 2 A)(2 A - 1) = 4 A - 2 + 4 ^2 A - 2 A = 4 ^2 A + 2 A - 2 = 2(2 ^2 A - 1) + 2 A Using the double angle identity 2A =

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