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 ArcSin

 http://functions.wolfram.com/01.12.27.0759.01

 Input Form

 ArcSin[(1 - z)/(1 + z)] == -2 ArcCot[Sqrt[1/z]] + (1/2) Pi /; Abs[Arg[z]] < Pi

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSin", "[", FractionBox[RowBox[List["1", "-", "z"]], RowBox[List["1", "+", "z"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", "2"]], RowBox[List["ArcCot", "[", SqrtBox[FractionBox["1", "z"]], "]"]]]], "+", RowBox[List[FractionBox["1", "2"], "\[Pi]"]]]]]], " ", "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", "z", "]"]], "]"]], "<", "\[Pi]"]]]]]]

 MathML Form

 sin - 1 ( 1 - z 1 + z ) π 2 - 2 cot - 1 ( 1 z ) /; "\[LeftBracketingBar]" arg ( z ) "\[RightBracketingBar]" < π Condition 1 -1 z 1 z -1 2 -1 -1 2 1 z -1 1 2 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", FractionBox[RowBox[List["1", "-", "z_"]], RowBox[List["1", "+", "z_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["ArcCot", "[", SqrtBox[FractionBox["1", "z"]], "]"]]]], "+", FractionBox["\[Pi]", "2"]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", "z", "]"]], "]"]], "<", "\[Pi]"]]]]]]]]

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

 2003-08-21