ArcTan[c x, c y] == ArcTan[x, y] /; c > 0

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["c", " ", "x"]], ",", RowBox[List["c", " ", "y"]]]], "]"]], "\[Equal]", RowBox[List["ArcTan", "[", RowBox[List["x", ",", "y"]], "]"]]]], "/;", RowBox[List["c", ">", "0"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mo> , </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> x </mi> <mo> , </mo> <mi> y </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> c </mi> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <arctan /> <apply> <times /> <ci> c </ci> <ci> x </ci> </apply> <apply> <times /> <ci> c </ci> <ci> y </ci> </apply> </apply> <apply> <arctan /> <ci> x </ci> <ci> y </ci> </apply> </apply> <apply> <gt /> <ci> c </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["c_", " ", "x_"]], ",", RowBox[List["c_", " ", "y_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ArcTan", "[", RowBox[List["x", ",", "y"]], "]"]], "/;", RowBox[List["c", ">", "0"]]]]]]]]

2007-05-02