Question
If ( ^ -1 x )= \ ^ -1 ( a b^2-a^2 ) \ b a, then x =
BITSAT
Mathematics
Inverse Trigonometric Functions
2024
BITSAT 2024 (Memory Based Paper 2)
BITSAT Mathematics Question (2024) — Solution
Options
- A. b 2 b^2-a^2
- B. b^2-a^2 a b
- C. a 2 b^2-a^2
- D. b^2-a^2 a
Answer
A. b 2 b^2-a^2
Step-by-step solution
Given that, ( ^ -1 x )= \ ^ -1 ( a b^2-a^2 ) \ Since, ^ -1 x= ^ -1 ( x 1-x^2 ) and ^ -1 x= ^ -1 ( 1+x^2 ) ( ^ -1 x 1-x^2 )= \ ^ -1 1+ ( a b^2-a^2 )^2 \ x 1-x^2 = b^2-a^2+a^2 b^2-a^2 x 1-x^2 = b b^2-a^2 On squaring both the sides, we get x^2 1-x^2 = b^2 b^2-a^2 aligned & x^2 b^2-x^2 a^2=b^2-b^2 x^2 \\ & x^2 b^2+b^2 x^2-x^2 a^2=b^2 aligned 2 x^2 b^2-x^2 a^2=b^2 x^2 (2 b^2-a^2 )=b^2 x= b 2 b^2-a^2
Related: Mathematics — Inverse Trigonometric Functions · All PYQ Banks