Cot[Pi/9] == Root[-1 + 33 #1^2 - 27 #1^4 + 3 #1^6 & , 6]

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> cot </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> &#960; </mi> <mn> 9 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <msubsup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ; </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 27 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 33 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 6 </mn> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <cot /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 9 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <ci> CompoundExpression </ci> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 27 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 33 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 6 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cot", "[", FractionBox["\[Pi]", "9"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Root", "[", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["33", " ", SuperscriptBox["#1", "2"]]], "-", RowBox[List["27", " ", SuperscriptBox["#1", "4"]]], "+", RowBox[List["3", " ", SuperscriptBox["#1", "6"]]]]], "&"]], ",", "6"]], "]"]]]]]]

2001-10-29