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 ArcSin

 http://functions.wolfram.com/01.12.27.0933.01

 Input Form

 ArcSin[Sqrt[(Sqrt[1 + z^2] - 1)/(2 Sqrt[1 + z^2])]] == (Sqrt[z^2]/(2 z)) ArcCot[1/z]

 Standard Form

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

 MathML Form

 sin - 1 ( 1 + z 2 - 1 2 1 + z 2 ) z 2 2 z cot - 1 ( 1 z ) 1 z 2 1 2 -1 2 1 z 2 1 2 -1 1 2 z 2 1 2 2 z -1 1 z -1 [/itex]

 Rule Form

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

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

 2003-08-21