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http://functions.wolfram.com/01.20.27.0013.01
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Cosh[z] == (1 - Tan[(I z)/2]^2)/(1 + Tan[(I z)/2]^2)
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Cell[BoxData[RowBox[List[RowBox[List["Cosh", "[", "z", "]"]], "\[Equal]", FractionBox[RowBox[List["1", "-", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], "2"], "]"]], "2"]]], RowBox[List["1", "+", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], "2"], "]"]], "2"]]]]]]]]
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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> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mi> tan </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <msup> <mi> tan </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <cosh /> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <tan /> <apply> <times /> <imaginaryi /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <tan /> <apply> <times /> <imaginaryi /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </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["Cosh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["1", "-", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], "2"], "]"]], "2"]]], RowBox[List["1", "+", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], "2"], "]"]], "2"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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