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 ArcCos

 http://functions.wolfram.com/01.13.16.0076.01

 Input Form

 ArcCos[Sqrt[1 - z^2]/Sqrt[-z^2]] == Pi/2 + ArcCos[1/z] /; Element[z, Reals] && 0 < z < 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCos", "[", FractionBox[SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]], SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["\[Pi]", "2"], "+", RowBox[List["ArcCos", "[", FractionBox["1", "z"], "]"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List["0", "<", "z", "<", "1"]]]], ")"]]]]]]

 MathML Form

 cos - 1 ( 1 - z 2 - z 2 ) cos - 1 ( 1 z ) + π 2 /; ( z 0 < z < 1 ) Condition 1 -1 z 2 1 2 -1 z 2 1 2 -1 1 z -1 2 -1 z 0 z 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCos", "[", FractionBox[SqrtBox[RowBox[List["1", "-", SuperscriptBox["z_", "2"]]]], SqrtBox[RowBox[List["-", SuperscriptBox["z_", "2"]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["\[Pi]", "2"], "+", RowBox[List["ArcCos", "[", FractionBox["1", "z"], "]"]]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List["0", "<", "z", "<", "1"]]]]]]]]]]

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

 2003-08-21