JEE Main20252 Apr 2025Evening ShiftMathematicsInverse Trigonometric FunctionsActual

If y= ( 3 + ⁻¹ x 2 ) , then (x-y)^2+3 y^2 is equal to _____.

Correct answer

Step-by-step solution

aligned & y= ( ⁻¹ 1 2 + ⁻¹ x 2 ) & y= 1 2 x 2 - 1- 1 4 1- x^2 4 & 4 y=x- 3 4-x^2 & 3 (4-x^2 )=x^2+16 y^2-8 x y & 12-3 x^2=x^2+16 y^2-8 x y & 4 x^2+16 y^2-8 x y=12 & x^2+4 y^2-2 x y=3 & x^2+y^2-2 x y-3 y^2=3 & (x-y)^2+3 y^2=3 aligned

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