Question
If ( ^ -1 (x 2 )) = ( ^ -1 1-x^2 ), x (0,1), then the value of x is :
JEE Main
Mathematics
Inverse Trigonometric Functions
2026
JEE Main 2026 (06 April Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 1 2
- B. 1 3
- C. 2 3
- D. 5 8
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
Related: Mathematics — Inverse Trigonometric Functions · All PYQ Banks