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 ArcCsc

 http://functions.wolfram.com/01.17.16.0103.01

 Input Form

 ArcCsc[Sqrt[2/(1 - Sqrt[1 - z^2])]] == (1/2) ArcCsc[1/z] /; Inequality[-(Pi/2), LessEqual, Arg[z], Less, Pi/2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCsc", "[", SqrtBox[RowBox[List[FractionBox["2", RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]]], " "]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["ArcCsc", "[", FractionBox["1", "z"], "]"]]]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "<", FractionBox["\[Pi]", "2"]]]]]]]

 MathML Form

 csc - 1 ( 2 1 - 1 - z 2 ) 1 2 csc - 1 ( 1 z ) /; - π 2 arg ( z ) < π 2 Condition 2 1 -1 1 -1 z 2 1 2 -1 1 2 1 2 1 z -1 Inequality -1 2 -1 z 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCsc", "[", SqrtBox[FractionBox["2", RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z_", "2"]]]]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["ArcCsc", "[", FractionBox["1", "z"], "]"]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "<", FractionBox["\[Pi]", "2"]]]]]]]]]

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

 2003-08-21