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JEE Main20244 Apr 2024Evening ShiftMathematicsInverse Trigonometric FunctionsActual

Given that the inverse trigonometric function assumes principal values only. Let x , y be any two real numbers in [-1,1] such that ⁻¹ x- ⁻¹ y= , - 2 . Then, the minimum value of x^2+y^2+2 x y is

Options

  1. A0
  2. B-1
  3. C1 2
  4. D- 1 2

Correct answer

A. 0

Step-by-step solution

aligned & ⁻¹ x- ( 2 - ⁻¹ y )= & ⁻¹ x+ ⁻¹ y= 2 + & [- 2 , ], 2 + [0, 3 2 ] & ⁻¹ (x y- 1-x^2 1-y^2 )= 2 + & x y- 1-x^2 1-y^2 =- & (x y+ )= (1-x^2 ) (1-y^2 ) & x^2 y^2+2 x y a+ ^2 a=1-x^2-y^2+x^2 y^2 & x^2+y^2+2 x y =1- ^2 & x^2+y^2+2 x y = ^2 aligned Min. value of ^2 =0 At = 2

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