Which is the correct fundamental period of cot inverse x?

[harini_5]

What is the fundamental period of cot inverse x?
The book, “TRIGONOMETRY “by S.L.Loney says it is –pi/2 to +pi/2 whereas IIT MATHEMATICS by M.L.Khanna says that is 0 to pi

 

[HallsofIvy]

If f is a non one-to-one function, then, in order to define its "inverse" you must restrict it to an interval on which it is one-to-one. Which such interval you choose is a matter of convention. And for tangent, those are two commonly used conventions.

 

[harini_5]

But examination point of view which one to choose?