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http://functions.wolfram.com/01.18.16.0127.01
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ArcSec[x] + ArcTan[y] ==
ArcSec[Sqrt[1 + y^2]/
((-1)^Floor[1/2 - Arg[(1/x - Sqrt[1 - 1/x^2] y)/Sqrt[1 + y^2]]/Pi]
(-Sqrt[1 - 1/x^2] - y/x))] -
(1/2) Pi ((-1)^Floor[1/2 - Arg[(1/x - Sqrt[1 - 1/x^2] y)/Sqrt[1 + y^2]]/
Pi] +
2 (1 + (-1)^Floor[1/2 - Arg[(1/x - Sqrt[1 - 1/x^2] y)/Sqrt[1 + y^2]]/Pi])
Floor[(Arg[Sqrt[1 - 1/x^2] + I/x] + Arg[(I + y)/Sqrt[1 + y^2]])/
(2 Pi)] -
2 (-1 + (-1)^Floor[1/2 - Arg[(1/x - Sqrt[1 - 1/x^2] y)/Sqrt[1 + y^2]]/
Pi]) Floor[1/2 - (Arg[Sqrt[1 - 1/x^2] + I/x] +
Arg[(I + y)/Sqrt[1 + y^2]])/(2 Pi)])
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSec", "[", "x", "]"]], "+", " ", RowBox[List["ArcTan", "[", "y", "]"]]]], "\[Equal]", RowBox[List[RowBox[List["ArcSec", "[", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["-", RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List["Arg", "[", FractionBox[RowBox[List[FractionBox["1", "x"], "-", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]], " ", "y"]]]], SqrtBox[RowBox[List["1", "+", SuperscriptBox["y", "2"]]]]], "]"]], "\[Pi]"]]], "]"]]]]], " ", SqrtBox[RowBox[List["1", "+", SuperscriptBox["y", "2"]]]]]], RowBox[List[RowBox[List["-", SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]]]], "-", FractionBox["y", "x"]]]], "]"]], "-", RowBox[List[FractionBox["1", "2"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List["Arg", "[", FractionBox[RowBox[List[FractionBox["1", "x"], "-", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]], " ", "y"]]]], SqrtBox[RowBox[List["1", "+", SuperscriptBox["y", "2"]]]]], "]"]], "\[Pi]"]]], "]"]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List["Arg", "[", FractionBox[RowBox[List[FractionBox["1", "x"], "-", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]], " ", "y"]]]], SqrtBox[RowBox[List["1", "+", SuperscriptBox["y", "2"]]]]], "]"]], "\[Pi]"]]], "]"]]]]], ")"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["Arg", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "x"]]], "]"]], "+", RowBox[List["Arg", "[", FractionBox[RowBox[List["\[ImaginaryI]", "+", "y"]], SqrtBox[RowBox[List["1", "+", SuperscriptBox["y", "2"]]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List["Arg", "[", FractionBox[RowBox[List[FractionBox["1", "x"], "-", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]], " ", "y"]]]], SqrtBox[RowBox[List["1", "+", SuperscriptBox["y", "2"]]]]], "]"]], "\[Pi]"]]], "]"]]]]], ")"]], " ", RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List[RowBox[List["Arg", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "x"]]], "]"]], "+", RowBox[List["Arg", "[", FractionBox[RowBox[List["\[ImaginaryI]", "+", "y"]], SqrtBox[RowBox[List["1", "+", SuperscriptBox["y", "2"]]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]]]]]], ")"]]]]]]]]]]
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<apply> <plus /> <apply> <power /> <ci> y </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> y </ci> <apply> <power /> <ci> x </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <pi /> <apply> <plus /> <apply> <times /> <cn 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Date Added to functions.wolfram.com (modification date)
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