JEE Main20266 April 2026Evening ShiftMathematicsInverse Trigonometric FunctionsActual

If ( ⁻¹(x 2 )) = ( ⁻¹ 1-x^2 ) , x (0,1) , then the value of x is :

Options

A1 2
B1 3
C2 3
D5 8

Correct answer

A. 1 2

Step-by-step solution

Let = ⁻¹(x 2 ) = x 2 From the right-angled triangle, = x 2 1+2x^2 Let = ⁻¹ 1-x^2 = 1-x^2 From the right-angled triangle, = 1 - (1-x^2) = x = = x 1-x^2 Given = , substituting the values: x 2 1+2x^2 = x 1-x^2 Since x (0,1) , x 0 . Dividing by x and squaring both sides: 2 1+2x^2 = 1 1-x^2 2(1-x^2) = 1+2x^2 2 - 2x^2 = 1 + 2x^2 4x^2 = 1 x^2 = 1 4 Since x (0,1) , x = 1 2 Answer: 1 2

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