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 Cot

 http://functions.wolfram.com/01.09.16.0033.01

 Input Form

 Cot[a + I b] == (Sin[2 a] - I Sinh[2 b])/(Cosh[2 b] - Cos[2 a])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Cot", "[", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], "]"]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["Sin", "[", RowBox[List["2", " ", "a"]], "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", "b"]], "]"]]]]]], RowBox[List[RowBox[List["Cosh", "[", RowBox[List["2", " ", "b"]], "]"]], "-", RowBox[List["Cos", "[", RowBox[List["2", " ", "a"]], "]"]]]]]]]]]

 MathML Form

 cot ( a + b ) sin ( 2 a ) - sinh ( 2 b ) cosh ( 2 b ) - cos ( 2 a ) a b 2 a -1 2 b 2 b -1 2 a -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cot", "[", RowBox[List["a_", "+", RowBox[List["\[ImaginaryI]", " ", "b_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["Sin", "[", RowBox[List["2", " ", "a"]], "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Sinh", "[", RowBox[List["2", " ", "b"]], "]"]]]]]], RowBox[List[RowBox[List["Cosh", "[", RowBox[List["2", " ", "b"]], "]"]], "-", RowBox[List["Cos", "[", RowBox[List["2", " ", "a"]], "]"]]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2001-10-29