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 ArcSin

 http://functions.wolfram.com/01.12.27.0816.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21