Question
If k= ( 4 + 1 2 ^ -1 ( 2 3 ) )+ ( 1 2 ^ -1 ( 2 3 ) ), then the number of solutions of the equation ^ -1 (k x-1)= ^ -1 x- ^ -1 x is \_\_\_\_
JEE Main
Mathematics
Inverse Trigonometric Functions
2026
JEE Main 2026 (28 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
Let = 1 2 ^ -1 2 3 , then 1 2 ^ -1 1 3 = ( 4 - ) k = + = 1 = 2 2 k = 2 2 3 = 3 ^ -1 (3x - 1) = ^ -1 x - ^ -1 x ^ -1 (3x - 1) = 2 - 2 ^ -1 x 3x - 1 = ( 2 - 2 ^ -1 x ) 3x - 1 = 2x^2 - 1 x = 0, 3 2 (rejected) No. of solution = 1
Related: Mathematics — Inverse Trigonometric Functions · All PYQ Banks