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MHT CET202210 Aug 2022Morning ShiftMathematicsInverse Trigonometric FunctionsActual

If ⁻¹ x- ⁻¹ y 2 = , where -1 x 1,-2 y 2, x y 2 , then for all x, y 4 x^2-4 x y a+y^2 is equal to

Options

  1. A2 ^2 a
  2. B4 ^2 a
  3. C4 ^2 a+2 x^2 y^2
  4. D4 ^2 a-2 x^2 y^2

Correct answer

B. 4 ^2 a

Step-by-step solution

aligned & ⁻¹ x- ⁻¹ y 2 =a & ⁻¹ (x y 2 + 1-x^2 1- y^2 4 )=a & x y 2 + (1-x^2 ) (4-y^2 ) 2 = a & (1-x^2 ) (4-y^2 )=2 a-x y & 4-y^2-4 x^2+x^2 y^2=4 ^2 a+x^2 y^2-4 a x y & 4-4 ^2 a=4 x^2-4 x y ^2 a+y^2 & 4 x^2-4 x y a+y^2=4 ^2 a aligned

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