Sin[Pi/8] == Sqrt[2 - Sqrt[2]]/2

Cell[BoxData[RowBox[List[RowBox[List["Sin", "[", FractionBox["\[Pi]", "8"], "]"]], "\[Equal]", FractionBox[SqrtBox[RowBox[List["2", "-", SqrtBox["2"]]]], "2"]]]]]

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

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sin", "[", FractionBox["\[Pi]", "8"], "]"]], "]"]], "\[RuleDelayed]", FractionBox[SqrtBox[RowBox[List["2", "-", SqrtBox["2"]]]], "2"]]]]]

2001-10-29