Which is the correct fundamental period of cot inverse x?

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The fundamental period of cot inverse x is debated, with S.L. Loney's "TRIGONOMETRY" stating it is from -π/2 to +π/2, while M.L. Khanna's "IIT MATHEMATICS" claims it is from 0 to π. The choice of interval is necessary for defining the inverse of a non one-to-one function and is largely a matter of convention. Both intervals are commonly accepted for tangent functions, leading to confusion regarding which to use in examinations. Ultimately, the selection of the interval may depend on the context or specific guidelines provided in academic settings.
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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
 
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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.
 
But examination point of view which one to choose?
 

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