Sec[(15 Pi)/8] == 2/Sqrt[2 + Sqrt[2]]

Cell[BoxData[RowBox[List[RowBox[List["Sec", "[", FractionBox[RowBox[List["15", "\[Pi]"]], "8"], "]"]], "\[Equal]", FractionBox["2", SqrtBox[RowBox[List["2", "+", SqrtBox["2"]]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> sec </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 8 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mn> 2 </mn> <msqrt> <mrow> <mn> 2 </mn> <mo> + </mo> <msqrt> <mn> 2 </mn> </msqrt> </mrow> </msqrt> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sec /> <apply> <times /> <cn type='integer'> 15 </cn> <pi /> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sec", "[", FractionBox[RowBox[List["15", " ", "\[Pi]"]], "8"], "]"]], "]"]], "\[RuleDelayed]", FractionBox["2", SqrtBox[RowBox[List["2", "+", SqrtBox["2"]]]]]]]]]

2001-10-29