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 Tan

 http://functions.wolfram.com/01.08.16.0033.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Tan", "[", 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["Cos", "[", RowBox[List["2", " ", "a"]], "]"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "b"]], "]"]]]]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Tan", "[", 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["Cos", "[", RowBox[List["2", " ", "a"]], "]"]], "+", RowBox[List["Cosh", "[", RowBox[List["2", " ", "b"]], "]"]]]]]]]]]

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

 2001-10-29