ArcSec[Csc[z]] == ArcCos[Sin[z]]

Cell[BoxData[RowBox[List[RowBox[List["ArcSec", "[", RowBox[List["Csc", "[", "z", "]"]], "]"]], "\[Equal]", RowBox[List["ArcCos", "[", RowBox[List["Sin", "[", "z", "]"]], "]"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> sec </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> csc </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <msup> <mi> cos </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arcsec /> <apply> <csc /> <ci> z </ci> </apply> </apply> <apply> <arccos /> <apply> <sin /> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSec", "[", RowBox[List["Csc", "[", "z_", "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["ArcCos", "[", RowBox[List["Sin", "[", "z", "]"]], "]"]]]]]]

2007-05-02