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 ArcSin

 http://functions.wolfram.com/01.12.27.0139.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2001-10-29