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 ArcSin

 http://functions.wolfram.com/01.12.27.0861.01

 Input Form

 ArcSin[1/Sqrt[z^2 + 1]] == Pi - ArcCot[z] /; Element[I z, Reals] && 0 < I z < 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSin", "[", FractionBox["1", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]]], "]"]], "\[Equal]", RowBox[List["\[Pi]", "-", RowBox[List["ArcCot", "[", "z", "]"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], "\[Element]", "Reals"]], "\[And]", RowBox[List["0", "<", RowBox[List["\[ImaginaryI]", " ", "z"]], "<", "1"]]]], ")"]]]]]]

 MathML Form

 sin - 1 ( 1 z 2 + 1 ) π - cot - 1 ( z ) /; ( z 0 < z < 1 ) Condition 1 z 2 1 1 2 -1 -1 z z 0 z 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", FractionBox["1", SqrtBox[RowBox[List[SuperscriptBox["z_", "2"], "+", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Pi]", "-", RowBox[List["ArcCot", "[", "z", "]"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], "\[Element]", "Reals"]], "&&", RowBox[List["0", "<", RowBox[List["\[ImaginaryI]", " ", "z"]], "<", "1"]]]]]]]]]]

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

 2003-08-21

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