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 ArcSin

 http://functions.wolfram.com/01.12.27.0016.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcSin", "[", RowBox[List["1", "-", RowBox[List["2", " ", SuperscriptBox["z", "2"]]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["\[Pi]", RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List[SqrtBox[SuperscriptBox["z", "2"]], " "]], "z"]]], ")"]]]], "+", RowBox[List[FractionBox[RowBox[List["2", " ", SqrtBox[SuperscriptBox["z", "2"]], " "]], "z"], RowBox[List["ArcCos", "[", "z", "]"]]]]]]]]]]

 MathML Form

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

 Rule Form

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

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

 2001-10-29