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JEE Main2005MathematicsInverse Trigonometric FunctionsActual

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

Options

  1. A2 2
  2. B4
  3. C4 ^2
  4. D-4 ^2

Correct answer

C. 4 ^2

Step-by-step solution

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

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