# Inverse Trigonometric Functions Class 12 Notes- Chapter 2

## What is Inverse Trigonometric Function?

The inverse trigonometric functions is an important aspect of trigonometric functions, included in the syllabus for class 12 students. Inverses of trigonometric functions exist solely due to the restrictions existing on the domains and their respective ranges. Being able to solve inverse trigonometric function problems starts by understanding the trigonometric ratios first.

The behavior of these trigonometric functions is usually represented in the form of graphical methods. They play an essential role in calculus as they help to define different integrals. The major applications of inverse trigonometric functions in everyday life are in the fields of science and engineering.

### What are the properties of Inverse Trigonometric Functions?

The properties of Inverse Trigonometric Functions help to prove a distinct relationship between the different trigonometric entities such as sinx, cosx, tanx, cosecx, secx, and cotx. The results obtained with the help of these properties are valid within the principal branches of the inverse trigonometric functions. These properties are valid for some values of x, where these inverse trigonometric functions are defined with.

### Important Questions

1. Find the principal values of the following:
2. $Cos^{-1}(-1/2)$ $Cosec^{-1}(2)$
1. Find the values of the following
2. $tan^{-1}(1)+cos^{-1}-1/2+sin^{-1}-1/2$
1. Find the values of the given equation
2. $cot(tan^{-1}a+cot^{-1}a)$
1. Solve the equations below
2. $2tan^{-1}(cos x)=tan^{-1}(2 cosec x)$
1. Solve $tan^{-1}2x+tan^{-1}3x=\pi /4$