Tanh[a] - Tanh[b] == Sech[a] Sech[b] Sinh[a - b]

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Tanh", "[", "a", "]"]], "-", RowBox[List["Tanh", "[", "b", "]"]]]], "\[Equal]", RowBox[List[RowBox[List["Sech", "[", "a", "]"]], " ", RowBox[List["Sech", "[", "b", "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["a", "-", "b"]], "]"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> tanh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> tanh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mi> sech </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sech </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <tanh /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <tanh /> <ci> b </ci> </apply> </apply> </apply> <apply> <times /> <apply> <sech /> <ci> a </ci> </apply> <apply> <sech /> <ci> b </ci> </apply> <apply> <sinh /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Tanh", "[", "a_", "]"]], "-", RowBox[List["Tanh", "[", "b_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Sech", "[", "a", "]"]], " ", RowBox[List["Sech", "[", "b", "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["a", "-", "b"]], "]"]]]]]]]]

2001-10-29