Inverse Trigonometric functions

Domain and range of inverse functions:

            Function           Domain               Range             

               Sin^-1x                      [-1,1]                        [-π/2,π/2] 

               Cos^-1x                     [-1,1]                           [0,π] 

               Tan^-1x                         R                          [-π/2,π/2] 

               Cot^-1x                         R                              [0,π] 

               Sec^-1x                     R-[-1,1]                      [0,π]-{π/2} 

               Cosec^-1x                 R-[-1,1]                     [-π/2,π/2]-{0}

 

COMPOSITION OF TRIGONOMETRIC FUNCTIONS AND THEIR INVERSE:

Sin^-1(sinX)=cos^-1(cosX)=tan^-1(tanX)=X 
                                              
  {provided 'X' is in the domain of the function.

SUM OF TWO INVERSE FUNCTIONS:

Sin^-1X+Cos^-1X=π/2

Tan^-1X+Cot^-1X=π/2

Sec^-1X+Cosec^-1X=π/2

RELATION BETWEEN TWO FUNCTIONS

Sin-1(1/x)=Cosec-1(x)

Cos^-1(1/x)=Sec^-1(x)

Tan^-1(1/x)=Cot^-1(x)