Question
Consider the following in respect of inverse circular functions : I. ^ -1 (-x)=- ^ -1 x II. ^ -1 (-x)= ^ -1 x III. ^ -1 (-x)= - ^ -1 x IV. ^ -1 (-x)= - ^ -1 x How many of the above are correct ?
NDA
Mathematics
Inverse Trigonometric Functions
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. One
- B. Two
- C. Three
- D. All the four
Answer
B. Two
Step-by-step solution
Statement I: ^ -1 (-x) = - ^ -1 x is a standard property of inverse trigonometric functions and is correct. Statement II: The correct property is ^ -1 (-x) = - ^ -1 x. Hence, this statement is incorrect. Statement III: The correct property is ^ -1 (-x) = - ^ -1 x. Hence, this statement is incorrect. Statement IV: ^ -1 (-x) = - ^ -1 x is a standard property and is correct. Exactly two of the given statements are correct.
Related: Mathematics — Inverse Trigonometric Functions · All PYQ Banks