Cos[z] == EllipticE[Pi/2 - z, 1] /; 0 <= Re[z] <= Pi

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Cos", "[", "z", "]"]], "\[Equal]", RowBox[List["EllipticE", "[", RowBox[List[RowBox[List[FractionBox["\[Pi]", "2"], "-", "z"]], ",", "1"]], "]"]]]], "/;", RowBox[List["0", "\[LessEqual]", RowBox[List["Re", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> E </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mfrac> <mi> &#960; </mi> <mn> 2 </mn> </mfrac> <mo> - </mo> <mi> z </mi> </mrow> <mo> &#10072; </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mn> 0 </mn> <mo> &#8804; </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mi> &#960; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <cos /> <ci> z </ci> </apply> <apply> <ci> EllipticE </ci> <apply> <plus /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <leq /> <cn type='integer'> 0 </cn> <apply> <real /> <ci> z </ci> </apply> <pi /> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cos", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["EllipticE", "[", RowBox[List[RowBox[List[FractionBox["\[Pi]", "2"], "-", "z"]], ",", "1"]], "]"]], "/;", RowBox[List["0", "\[LessEqual]", RowBox[List["Re", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]]]

2001-10-29