Cos[z] + Sin[z] == Sqrt[2] Cos[z - Pi/4]

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Cos", "[", "z", "]"]], "+", " ", RowBox[List["Sin", "[", "z", "]"]]]], "\[Equal]", RowBox[List[SqrtBox["2"], RowBox[List["Cos", "[", RowBox[List["z", "-", FractionBox["\[Pi]", "4"]]], "]"]]]]]]]]

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

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Cos", "[", "z_", "]"]], "+", RowBox[List["Sin", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox["2"], " ", RowBox[List["Cos", "[", RowBox[List["z", "-", FractionBox["\[Pi]", "4"]]], "]"]]]]]]]]

2003-08-21