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 ArcCos

 http://functions.wolfram.com/01.13.16.0055.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21

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