NCERT Class 12 Maths
Chapter 2: Inverse Trigonometric Functions
14 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions — Miscellaneous Exercise
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Evaluate cos⁻¹(cos(13π/6)).
Question 2
Evaluate tan⁻¹(tan(7π/6)).
Question 3
Prove 2sin⁻¹(3/5)=tan⁻¹(24/7).
Question 4
Prove sin⁻¹(8/17)+sin⁻¹(3/5)=tan⁻¹(77/36).
Question 5
Prove cos⁻¹(4/5)+cos⁻¹(12/13)=cos⁻¹(33/65).
Question 6
Prove cos⁻¹(12/13)+sin⁻¹(3/5)=sin⁻¹(56/65).
Question 7
Prove tan⁻¹(63/16)=sin⁻¹(5/13)+cos⁻¹(3/5).
Question 8
Prove tan⁻¹√x=(1/2)cos⁻¹((1−x)/(1+x)), 0≤x≤1.
Question 9
Prove cot⁻¹((√(1+sin x)+√(1−sin x))/(√(1+sin x)−√(1−sin x)))=x/2 for 0<x<π/4.
Question 10
Prove tan⁻¹((√(1+x)−√(1−x))/(√(1+x)+√(1−x)))=π/4−(1/2)cos⁻¹x for −1/√2≤x≤1.
Question 11
Solve 2tan⁻¹(cos x)=tan⁻¹(2cosec x) over all real x for which the equation is defined.
Question 12
Solve tan⁻¹((1−x)/(1+x))=(1/2)tan⁻¹x, x>0.
Question 13
For |x|<1, evaluate sin(tan⁻¹x).
Question 14
Solve sin⁻¹(1−x)−2sin⁻¹x=π/2.