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 Cot

 http://functions.wolfram.com/01.09.03.0051.01

 Input Form

 Cot[(5 Pi)/7] == (4 (14 - 42 I Sqrt[3])^(1/3) + 2^(1/3) (4 I Sqrt[7] (14 - I Sqrt[7] - 3 Sqrt[21])^(1/3) + (1 - I Sqrt[3]) (14 - I Sqrt[7] - 3 Sqrt[21])^(2/3) (28 + 2 I Sqrt[7] + 6 Sqrt[21])^(1/3) - 2 (14 + I Sqrt[7] + 3 Sqrt[21])^(1/3) ((-I) Sqrt[7] + Sqrt[21] + (28 - 84 I Sqrt[3])^(1/3))))/(4 7^(5/6) (2 - 6 I Sqrt[3])^(1/3) + 2^(1/3) (4 Sqrt[7] (14 - I Sqrt[7] - 3 Sqrt[21])^(1/3) + (I + Sqrt[3]) (14 - I Sqrt[7] - 3 Sqrt[21])^(2/3) (28 + 2 I Sqrt[7] + 6 Sqrt[21])^(1/3) + 2 I (14 + I Sqrt[7] + 3 Sqrt[21])^(1/3) (I Sqrt[7] - Sqrt[21] + (28 - 84 I Sqrt[3])^(1/3))))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Cot", "[", FractionBox[RowBox[List["5", " ", "\[Pi]"]], "7"], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["4", " ", 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["4", " ", "\[ImaginaryI]", " ", 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["1", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", 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["2", " ", 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["7"]]], "+", SqrtBox["21"], "+", SuperscriptBox[RowBox[List["(", RowBox[List["28", "-", RowBox[List["84", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], ")"]]]]]], ")"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["4", " ", 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["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["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", 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["2", " ", "\[ImaginaryI]", " ", 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["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", SqrtBox["21"], "+", SuperscriptBox[RowBox[List["(", RowBox[List["28", "-", RowBox[List["84", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

 cot ( 5 π 7 ) ( 4 14 - 42 3 3 + 2 3 ( - 2 ( 28 - 84 3 3 + 7 ( - ) + 21 ) 14 + 7 + 3 21 3 + ( 1 - 3 ) 28 + 2 7 + 6 21 3 ( 14 - 7 - 3 21 ) 2 / 3 + 4 7 14 - 7 - 3 21 3 ) ) / ( 4 7 5 / 6 2 - 6 3 3 + 2 3 ( 2 ( 28 - 84 3 3 + 7 - 21 ) 14 + 7 + 3 21 3 + 4 7 14 - 7 - 3 21 3 + ( + 3 ) 28 + 2 7 + 6 21 3 ( 14 - 7 - 3 21 ) 2 / 3 ) ) 5 7 -1 4 14 -1 42 3 1 2 1 3 2 1 3 -2 28 -1 84 3 1 2 1 3 7 1 2 -1 21 1 2 14 7 1 2 3 21 1 2 1 3 1 -1 3 1 2 28 2 7 1 2 6 21 1 2 1 3 14 -1 7 1 2 -1 3 21 1 2 2 3 4 7 1 2 14 -1 7 1 2 -1 3 21 1 2 1 3 4 7 5 6 2 -1 6 3 1 2 1 3 2 1 3 2 28 -1 84 3 1 2 1 3 7 1 2 -1 21 1 2 14 7 1 2 3 21 1 2 1 3 4 7 1 2 14 -1 7 1 2 -1 3 21 1 2 1 3 3 1 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 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cot", "[", FractionBox[RowBox[List["5", " ", "\[Pi]"]], "7"], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["4", " ", 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["4", " ", "\[ImaginaryI]", " ", 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["1", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", 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["2", " ", 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["7"]]], "+", SqrtBox["21"], "+", SuperscriptBox[RowBox[List["(", RowBox[List["28", "-", RowBox[List["84", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], ")"]]]]]], ")"]]]]]], RowBox[List[RowBox[List["4", " ", 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["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["\[ImaginaryI]", "+", SqrtBox["3"]]], ")"]], " ", 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["2", " ", "\[ImaginaryI]", " ", 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["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", SqrtBox["21"], "+", SuperscriptBox[RowBox[List["(", RowBox[List["28", "-", RowBox[List["84", " ", "\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], ")"]]]]]], ")"]]]]]]]]]]]

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

 2001-10-29