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Manipal MET2015MathematicsInverse Trigonometric Functions

If ⁻¹ x 2 + ⁻¹ y 3 = , then 9 x^2-12 x y +4 y^2 is equal to

Options

  1. A36
  2. B-36 ^2
  3. C36 ^2
  4. D36 ^2

Correct answer

C. 36 ^2

Step-by-step solution

We have, ⁻¹ x 2 + ⁻¹ y 3 = aligned & ⁻¹ x y 6 - 1- x^2 4 1- y^2 9 = & x y- 4-x^2 9-y^2 =6 & (x y-6 )^2= (4-x^2 ) (9-y^2 ) & -12 x y +36 ^2 =36-4 y^2-9 x^2 & 9 x^2+4 y^2-12 x y =36 ^2 aligned

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