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 ArcSin

 http://functions.wolfram.com/01.12.27.0145.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2001-10-29