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 Cot

 http://functions.wolfram.com/01.09.03.0031.01

 Input Form

 Cot[(3 Pi)/7] == (-4 I (14 - 42 I Sqrt[3])^(1/3) + 2^(1/3) (2 I Sqrt[7] (I + Sqrt[3]) (14 - I Sqrt[7] - 3 Sqrt[21])^(1/3) - 4 Sqrt[7] (14 + I Sqrt[7] + 3 Sqrt[21])^(1/3) + (-I + Sqrt[3]) (28 - 2 I Sqrt[7] - 6 Sqrt[21])^(1/3) (14 + I Sqrt[7] + 3 Sqrt[21])^(2/3) + 2 I (14 - I Sqrt[7] - 3 Sqrt[21])^(2/3) (28 + 2 I Sqrt[7] + 6 Sqrt[21])^ (1/3)))/(-4 I 7^(5/6) (2 - 6 I Sqrt[3])^(1/3) + 2^(1/3) (2 Sqrt[7] (I + Sqrt[3]) (14 - I Sqrt[7] - 3 Sqrt[21])^(1/3) - 2 (14 - I Sqrt[7] - 3 Sqrt[21])^(2/3) (28 + 2 I Sqrt[7] + 6 Sqrt[21])^ (1/3) - I (98 + 7 I Sqrt[7] + 21 Sqrt[21])^(1/3) (4 7^(1/6) + 2^(2/3) (1 - 3 I Sqrt[3])^(1/3) (-I + Sqrt[3]))))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Cot", "[", FractionBox[RowBox[List["3", " ", "\[Pi]"]], "7"], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["42", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["7"], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "-", RowBox[List["4", " ", SqrtBox["7"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["28", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["6", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["2", "/", "3"]]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["28", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["6", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "\[ImaginaryI]", " ", SuperscriptBox["7", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["2", "-", RowBox[List["6", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SqrtBox["7"], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "-", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["28", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["6", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["98", "+", RowBox[List["7", " ", "\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["21", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", SuperscriptBox["7", RowBox[List["1", "/", "6"]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

 cot ( 3 π 7 ) ( 2 3 ( - 4 7 14 + 7 + 3 21 3 + ( - + 3 ) 28 - 2 7 - 6 21 3 ( 14 + 7 + 3 21 ) 2 / 3 + 2 7 ( + 3 ) 14 - 7 - 3 21 3 + 2 28 + 2 7 + 6 21 3 ( 14 - 7 - 3 21 ) 2 / 3 ) - 4 14 - 42 3 3 ) / ( 2 3 ( - 2 ( 14 - 7 - 3 21 ) 2 / 3 28 + 2 7 + 6 21 3 + 2 7 ( + 3 ) 14 - 7 - 3 21 3 - 98 + 7 7 + 21 21 3 ( 2 2 / 3 ( - + 3 ) 1 - 3 3 3 + 4 7 6 ) ) - 4 7 5 / 6 2 - 6 3 3 ) 3 7 -1 2 1 3 -4 7 1 2 14 7 1 2 3 21 1 2 1 3 -1 3 1 2 28 -1 2 7 1 2 -1 6 21 1 2 1 3 14 7 1 2 3 21 1 2 2 3 2 7 1 2 3 1 2 14 -1 7 1 2 -1 3 21 1 2 1 3 2 28 2 7 1 2 6 21 1 2 1 3 14 -1 7 1 2 -1 3 21 1 2 2 3 -1 4 14 -1 42 3 1 2 1 3 2 1 3 -2 14 -1 7 1 2 -1 3 21 1 2 2 3 28 2 7 1 2 6 21 1 2 1 3 2 7 1 2 3 1 2 14 -1 7 1 2 -1 3 21 1 2 1 3 -1 98 7 7 1 2 21 21 1 2 1 3 2 2 3 -1 3 1 2 1 -1 3 3 1 2 1 3 4 7 1 6 -1 4 7 5 6 2 -1 6 3 1 2 1 3 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cot", "[", FractionBox[RowBox[List["3", " ", "\[Pi]"]], "7"], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["42", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["7"], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "-", RowBox[List["4", " ", SqrtBox["7"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["28", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["6", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["2", "/", "3"]]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["28", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["6", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]]]]]], RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "\[ImaginaryI]", " ", SuperscriptBox["7", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["2", "-", RowBox[List["6", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SqrtBox["7"], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "-", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["28", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["6", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["98", "+", RowBox[List["7", " ", "\[ImaginaryI]", " ", SqrtBox["7"]]], "+", RowBox[List["21", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", SuperscriptBox["7", RowBox[List["1", "/", "6"]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]]]]]], ")"]]]]]], ")"]]]]]]]]]]]

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

 2001-10-29