Class 12 Maths Inverse Trigonometric Functions Inverse of Cot function

Inverse of Cot function

• Natural domain & Range of cot function, cot : R – { x : x = nπ, n Z} → R
• If we restrict domain to [0, π], then it becomes one-one & onto with range R
• Restricted domain & range of cot function, cot : [ 0, π ] → R
• Restricted domain & range of cot-1 function, cot-1 : R à [ 0, π ]
• Actually, cot function restricted to any of the intervals [– π, 0], [π, 2π] , is one-one & its range is R. Corresponding to each such interval, we get a branch of function cot–1. The branch with range , [0, π ], is called principal value branch
• If y = cot–1 x, then cot y = x.
• Thus, the graph of cot–1 function can be obtained from the graph of original function by interchanging x and y axes, i.e., if (a, b) is a point on  the graph of cot function, then (b, a) becomes the corresponding point on the graph of inverse of cot function

Note:

• sin–1x should not be confused with (sin x)–1. In fact (sin x)–1 = 1/ sin x and similarly for other trigonometric functions.
• Whenever no branch of inverse trigonometric functions is mentioned, we mean the principal value branch of that function.
• The value of an inverse trigonometric functions which lies in the range of principal branch is called the principal value of that inverse trigonometric functions

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