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http://functions.wolfram.com/01.09.16.0063.01
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Cot[a] + I Coth[b] == I Csc[a] Csch[b] Sin[a - I b]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Cot", "[", "a", "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Coth", "[", "b", "]"]]]]]], "\[Equal]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Csc", "[", "a", "]"]], " ", RowBox[List["Csch", "[", "b", "]"]], " ", RowBox[List["Sin", "[", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "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> cot </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> coth </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> csc </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> csch </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <cot /> <ci> a </ci> </apply> <apply> <times /> <imaginaryi /> <apply> <coth /> <ci> b </ci> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <csc /> <ci> a </ci> </apply> <apply> <csch /> <ci> b </ci> </apply> <apply> <sin /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Cot", "[", "a_", "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Coth", "[", "b_", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Csc", "[", "a", "]"]], " ", RowBox[List["Csch", "[", "b", "]"]], " ", RowBox[List["Sin", "[", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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