Question
If k is a root of x^2 - 4x + 1 = 0, then what is ^ -1 k + ^ -1 1 k equal to?
NDA
Mathematics
Inverse Trigonometric Functions
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. - 2
- B. 0
- C. 4
- D. 2
Answer
D. 2
Step-by-step solution
The given equation is x^2 - 4x + 1 = 0. The roots of the equation are given by x = 4 16 - 4 2 = 2 3 . Since 3 1.732, both roots 2 + 3 and 2 - 3 are positive. Therefore, k > 0. Using the standard inverse trigonometric identity for x > 0: ^ -1 x + ^ -1 ( 1 x ) = 2 Substituting x = k, we get: ^ -1 k + ^ -1 ( 1 k ) = 2 Answer: 2
Related: Mathematics — Inverse Trigonometric Functions · All PYQ Banks