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 ArcSin

 http://functions.wolfram.com/01.12.27.0194.01

 Input Form

 ArcSin[Sqrt[(z - 1)/(2 z)]] == (1/(2 Sqrt[1/z - 1])) Sqrt[1 - 1/z] ArcCosh[1/z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcSin", "[", SqrtBox[FractionBox[RowBox[List["z", "-", "1"]], RowBox[List["2", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", SqrtBox[RowBox[List[FractionBox["1", "z"], "-", "1"]]]]]], SqrtBox[RowBox[List["1", "-", FractionBox["1", "z"]]]], " ", RowBox[List["ArcCosh", "[", FractionBox["1", "z"], "]"]]]]]]]]

 MathML Form

 sin - 1 ( z - 1 2 z ) 1 2 1 z - 1 1 - 1 z cosh - 1 ( 1 z ) z -1 2 z -1 1 2 1 2 1 z -1 -1 1 2 -1 1 -1 1 z -1 1 2 1 z -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", SqrtBox[FractionBox[RowBox[List["z_", "-", "1"]], RowBox[List["2", " ", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", "z"]]]], " ", RowBox[List["ArcCosh", "[", FractionBox["1", "z"], "]"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[FractionBox["1", "z"], "-", "1"]]]]]]]]]]

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

 2001-10-29