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Csc






Mathematica Notation

Traditional Notation









Elementary Functions > Csc[z] > Identities > Functional identities





http://functions.wolfram.com/01.10.17.0002.01









  


  










Input Form





(Csc[Subscript[z, 1]]^2 - Csc[Subscript[z, 2]]^2)^2 Csc[Subscript[z, 1] + Subscript[z, 2]]^4 - 2 Csc[Subscript[z, 1]]^2 Csc[Subscript[z, 2]]^2 (Csc[Subscript[z, 1]]^2 + Csc[Subscript[z, 2]]^2 - 2) Csc[Subscript[z, 1] + Subscript[z, 2]]^2 + Csc[Subscript[z, 1]]^4 Csc[Subscript[z, 2]]^4 == 0










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["Csc", "[", SubscriptBox["z", "1"], "]"]], "2"], "-", SuperscriptBox[RowBox[List["Csc", "[", SubscriptBox["z", "2"], "]"]], "2"]]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["Csc", "[", RowBox[List[SubscriptBox["z", "1"], "+", SubscriptBox["z", "2"]]], "]"]], "4"]]], "-", RowBox[List["2", " ", SuperscriptBox[RowBox[List["Csc", "[", SubscriptBox["z", "1"], "]"]], "2"], " ", SuperscriptBox[RowBox[List["Csc", "[", SubscriptBox["z", "2"], "]"]], "2"], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["Csc", "[", SubscriptBox["z", "1"], "]"]], "2"], "+", SuperscriptBox[RowBox[List["Csc", "[", SubscriptBox["z", "2"], "]"]], "2"], "-", "2"]], ")"]], " ", SuperscriptBox[RowBox[List["Csc", "[", RowBox[List[SubscriptBox["z", "1"], "+", SubscriptBox["z", "2"]]], "]"]], "2"]]], "+", RowBox[List[SuperscriptBox[RowBox[List["Csc", "[", SubscriptBox["z", "1"], "]"]], "4"], " ", SuperscriptBox[RowBox[List["Csc", "[", SubscriptBox["z", "2"], "]"]], "4"]]]]], "\[Equal]", "0"]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mrow> <msup> <mi> csc </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> csc </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> csc </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> csc </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msup> <mi> csc </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> csc </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> csc </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> csc </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <msup> <mi> csc </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <msup> <mi> csc </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <csc /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <csc /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <csc /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <power /> <apply> <csc /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <csc /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -2 </cn> </apply> <apply> <power /> <apply> <csc /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <csc /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <csc /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <csc /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <csc /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["Csc", "[", SubscriptBox["z_", "1"], "]"]], "2"], "-", SuperscriptBox[RowBox[List["Csc", "[", SubscriptBox["z_", "2"], "]"]], "2"]]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["Csc", "[", RowBox[List[SubscriptBox["z_", "1"], "+", SubscriptBox["z_", "2"]]], "]"]], "4"]]], "-", RowBox[List["2", " ", SuperscriptBox[RowBox[List["Csc", "[", SubscriptBox["z_", "1"], "]"]], "2"], " ", SuperscriptBox[RowBox[List["Csc", "[", SubscriptBox["z_", "2"], "]"]], "2"], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["Csc", "[", SubscriptBox["z_", "1"], "]"]], "2"], "+", SuperscriptBox[RowBox[List["Csc", "[", SubscriptBox["z_", "2"], "]"]], "2"], "-", "2"]], ")"]], " ", SuperscriptBox[RowBox[List["Csc", "[", RowBox[List[SubscriptBox["z_", "1"], "+", SubscriptBox["z_", "2"]]], "]"]], "2"]]], "+", RowBox[List[SuperscriptBox[RowBox[List["Csc", "[", SubscriptBox["z_", "1"], "]"]], "4"], " ", SuperscriptBox[RowBox[List["Csc", "[", SubscriptBox["z_", "2"], "]"]], "4"]]]]], "]"]], "\[RuleDelayed]", "0"]]]]










Date Added to functions.wolfram.com (modification date)





2001-10-29





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