Cosh[z]^2 + Sinh[z]^2 == Cosh[2 z]

Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["Cosh", "[", "z", "]"]], "2"], "+", SuperscriptBox[RowBox[List["Sinh", "[", "z", "]"]], "2"]]], "\[Equal]", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]]]]

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

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox[RowBox[List["Cosh", "[", "z_", "]"]], "2"], "+", SuperscriptBox[RowBox[List["Sinh", "[", "z_", "]"]], "2"]]], "]"]], "\[RuleDelayed]", RowBox[List["Cosh", "[", RowBox[List["2", " ", "z"]], "]"]]]]]]

2001-10-29