NCERT Class 12 Maths
Chapter 2: Inverse Trigonometric Functions
15 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions — Exercise 2.2
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Prove 3sin⁻¹x=sin⁻¹(3x−4x³) for −1/2≤x≤1/2.
Question 2
Prove 3cos⁻¹x=cos⁻¹(4x³−3x) for 1/2≤x≤1.
Question 3
Simplify tan⁻¹((√(1+x²)−1)/x), x≠0.
Question 4
Simplify tan⁻¹√((1−cos x)/(1+cos x)), 0<x<π.
Question 5
Simplify tan⁻¹((cos x−sin x)/(cos x+sin x)), −π/4<x<3π/4.
Question 6
Simplify tan⁻¹(x/√(a²−x²)), |x|<a.
Question 7
Simplify tan⁻¹((3a²x−x³)/(a³−3ax²)), a>0, −a/√3<x<a/√3.
Question 8
Evaluate tan⁻¹[2cos(2sin⁻¹(1/2))].
Question 9
Evaluate tan{(1/2)[sin⁻¹(2x/(1+x²))+cos⁻¹((1−y²)/(1+y²))]}, |x| 0, xy<1.
Question 10
Evaluate sin⁻¹(sin(2π/3)).
Question 11
Evaluate tan⁻¹(tan(3π/4)).
Question 12
Evaluate tan(sin⁻¹(3/5)+cot⁻¹(3/2)).
Question 13
Evaluate cos⁻¹(cos(7π/6)).
Question 14
Evaluate sin(π/3−sin⁻¹(−1/2)).
Question 15
Evaluate tan⁻¹(√3)−cot⁻¹(−√3).