Question
Let 0 < < 1, = 1 3 and ^ -1 (1- ) + ^ -1 (1- ) = 4 . Then 6( + ) is equal to:
JEE Main
Mathematics
Inverse Trigonometric Functions
2026
JEE Main 2026 (06 April Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 6
- B. 7
- C. 8
- D. 9
Answer
B. 7
Step-by-step solution
Given ^ -1 (1- ) + ^ -1 (1- ) = 4 Applying the formula ^ -1 x + ^ -1 y = ^ -1 ( x+y 1-xy ), we get: (1- ) + (1- ) 1 - (1- )(1- ) = ( 4 ) = 1 2 - - = 1 - (1 - - + ) 2 - - = + - 2( + ) = 2 + Given = 1 3 , we have = 1 3 . Substituting this into the equation: 2( + ) = 2 + 1 3 2( + ) = 7 3 + = 7 6 Therefore, 6( + ) = 6 7 6 = 7 Answer: 7
Related: Mathematics — Inverse Trigonometric Functions · All PYQ Banks