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http://functions.wolfram.com/01.16.16.0010.01
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ArcCot[x] - ArcCot[y] == (-(Pi/2)) Sign[x - y] Sign[x y] +
ArcCot[(x - y)/(1 + x y)] /; x y != -1
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["ArcCot", "[", "x", "]"]], "-", RowBox[List["ArcCot", "[", "y", "]"]]]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], " ", RowBox[List["Sign", "[", RowBox[List["x", "-", "y"]], "]"]], " ", RowBox[List["Sign", "[", RowBox[List["x", " ", "y"]], "]"]]]], "+", RowBox[List["ArcCot", "[", FractionBox[RowBox[List["x", "-", "y"]], RowBox[List["1", "+", RowBox[List["x", " ", "y"]]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["x", " ", "y"]], "\[NotEqual]", RowBox[List["-", "1"]]]]]]]]
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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> <mrow> <msup> <mi> cot </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <msup> <mi> cot </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> y </mi> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <msup> <mi> cot </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> x </mi> <mo> - </mo> <mi> y </mi> </mrow> <mrow> <mrow> <mi> x </mi> <mo> ⁢ </mo> <mi> y </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mi> sgn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> x </mi> <mo> - </mo> <mi> y </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sgn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> x </mi> <mo> ⁢ </mo> <mi> y </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> x </mi> <mo> ⁢ </mo> <mi> y </mi> </mrow> <mo> ≠ </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <arccot /> <ci> x </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <arccot /> <ci> y </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <arccot /> <apply> <times /> <apply> <plus /> <ci> x </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> y </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> x </ci> <ci> y </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Sign </ci> <apply> <plus /> <ci> x </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> y </ci> </apply> </apply> </apply> <apply> <ci> Sign </ci> <apply> <times /> <ci> x </ci> <ci> y </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <neq /> <apply> <times /> <ci> x </ci> <ci> y </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["ArcCot", "[", "x_", "]"]], "-", RowBox[List["ArcCot", "[", "y_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["-", "\[Pi]"]], ")"]], " ", RowBox[List["Sign", "[", RowBox[List["x", "-", "y"]], "]"]], " ", RowBox[List["Sign", "[", RowBox[List["x", " ", "y"]], "]"]]]], "+", RowBox[List["ArcCot", "[", FractionBox[RowBox[List["x", "-", "y"]], RowBox[List["1", "+", RowBox[List["x", " ", "y"]]]]], "]"]]]], "/;", RowBox[List[RowBox[List["x", " ", "y"]], "\[NotEqual]", RowBox[List["-", "1"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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