Question
Consider the following for the two (02) items that follow: Let y = ^ -1 (x - 4x^3 27 ). What is y equal to?
NDA
Mathematics
Inverse Trigonometric Functions
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. ^ -1 x
- B. ^ -1 ( x 3 )
- C. 3 ^ -1 x
- D. 3 ^ -1 ( x 3 )
Answer
D. 3 ^ -1 ( x 3 )
Step-by-step solution
Given y = ^ -1 (x - 4x^3 27 ) Substitute x = 3 , which gives = x 3 or = ^ -1 ( x 3 ) The expression becomes: y = ^ -1 (3 - 4(3 )^3 27 ) y = ^ -1 (3 - 4(27 ^3 ) 27 ) y = ^ -1 (3 - 4 ^3 ) Using the trigonometric identity (3 ) = 3 - 4 ^3 : y = ^ -1 ( (3 )) y = 3 Substituting back the value of : y = 3 ^ -1 ( x 3 ) Answer: 3 ^ -1 ( x 3 )
Related: Mathematics — Inverse Trigonometric Functions · All PYQ Banks