Basics Of Inverse Trigonometric Functions

In mathematics, INVERSE TRIGONOMETRIC FUNCTIONS are inverse functions of the TRIGONOMETRIC FUNCTIONS with appropriate restrain domain. Inverse trigonometric function is also known as ANTI TRIGONOMETRIC FUNCTION (occasionally called as CYCLOMETRIC FUNCTION).
The representations sin-1, cos-1 is often using for arcsine, arccos etc but this precept logically conflicts with the common linguistics for expression like sin2(x), which denotes to numeric power rather than a function composition.
INVERSE TRIGONOMETRIC FUNCTION: Following table explains the basic inverse trig functions with their notations and domains.

DERIVATIVES OF INVERSE TRIG FUNCTIONS: 

Derivative of Inverse trigonometric Functions which are commonly used are as follows

Values of generic Inverse Trig Functions Derivatives can be used to solve complex equations using chain rule. 

INTEGRALS OF INVERSE TRIG FUNCTIONS: The integrals of the inverse trig functions can be finding out by integrating the derivative and applying definite values to it. 

IDENTITIES USED IN TRIGONOMETRY

Sin² x+ cos² x = 1

1 + tan² x = sec² x

1 + cot² x =csc² x