Coth[z/2] == Sinh[z]/(Cosh[z] - 1)

Cell[BoxData[RowBox[List[RowBox[List["Coth", "[", FractionBox["z", "2"], "]"]], "\[Equal]", FractionBox[RowBox[List["Sinh", "[", "z", "]"]], RowBox[List[RowBox[List["Cosh", "[", "z", "]"]], "-", "1"]]]]]]]

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

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Coth", "[", FractionBox["z_", "2"], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["Sinh", "[", "z", "]"]], RowBox[List[RowBox[List["Cosh", "[", "z", "]"]], "-", "1"]]]]]]]

2001-10-29