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http://functions.wolfram.com/01.21.16.0044.01
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Tanh[a] Coth[b] == (Sinh[a + b] + Sinh[a - b])/(Sinh[a + b] - Sinh[a - b])
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Tanh", "[", "a", "]"]], " ", RowBox[List["Coth", "[", "b", "]"]]]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["Sinh", "[", RowBox[List["a", "+", "b"]], "]"]], "+", RowBox[List["Sinh", "[", RowBox[List["a", "-", "b"]], "]"]]]], RowBox[List[RowBox[List["Sinh", "[", RowBox[List["a", "+", "b"]], "]"]], "-", RowBox[List["Sinh", "[", RowBox[List["a", "-", "b"]], "]"]]]]]]]]]
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<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> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> coth </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <tanh /> <ci> a </ci> </apply> <apply> <coth /> <ci> b </ci> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <sinh /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <sinh /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <sinh /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <sinh /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Tanh", "[", "a_", "]"]], " ", RowBox[List["Coth", "[", "b_", "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["Sinh", "[", RowBox[List["a", "+", "b"]], "]"]], "+", RowBox[List["Sinh", "[", RowBox[List["a", "-", "b"]], "]"]]]], RowBox[List[RowBox[List["Sinh", "[", RowBox[List["a", "+", "b"]], "]"]], "-", RowBox[List["Sinh", "[", RowBox[List["a", "-", "b"]], "]"]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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