Cos[Pi/30] == (1/4) Sqrt[(5 - Sqrt[5])/2] + ((Sqrt[5] + 1)/8) Sqrt[3]

Cell[BoxData[RowBox[List[RowBox[List["Cos", "[", FractionBox["\[Pi]", "30"], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", SqrtBox[FractionBox[RowBox[List["5", "-", SqrtBox["5"]]], "2"]]]], "+", RowBox[List[FractionBox[RowBox[List[SqrtBox["5"], "+", "1"]], "8"], " ", SqrtBox["3"], " "]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> &#960; </mi> <mn> 30 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> &#8290; </mo> <msqrt> <mfrac> <mrow> <mn> 5 </mn> <mo> - </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> <mn> 2 </mn> </mfrac> </msqrt> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <msqrt> <mn> 5 </mn> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <msqrt> <mn> 3 </mn> </msqrt> <mtext> </mtext> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <cos /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 30 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <plus /> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cos", "[", FractionBox["\[Pi]", "30"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", SqrtBox[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["5", "-", SqrtBox["5"]]], ")"]]]]]]], "+", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[SqrtBox["5"], "+", "1"]], ")"]], " ", SqrtBox["3"]]]]]]]]]

2001-10-29