, is bijective and its range is the set of all real numbers R – (–1, 1) Fig 2 2 (i)
Rationalised 2023-24
 22
MATHEMATICS
Thus cosec–1 can be defined as a function whose domain is R – (–1, 1) and range could
be any of the intervals 
−
−


 − −
23
2
π
π
π
,
{
}, 
−

2π π −
2
0
,
{ }, 
,3
{ }
2
2
π
π

 − π




etc The
function corresponding to the range 
,
{0}
2
−π π2
 −




is called the principal value branch
of cosec–1