Inverse secant: Representations through equivalent functions (formula 01.18.27.0892)

ArcSec

$Mathematica Notation$

Elementary Functions

Representations through equivalent functions

With related functions

Involving csc^-1

Involving sec^-1(1/1-2z²)

Involving sec^-1(1/1-2 z²) and csc^-1(1/z)

http://functions.wolfram.com/01.18.27.0892.01

Input Form

ArcSec[1/(1 - 2 z^2)] == 2 (Sqrt[z^2]/z) ArcCsc[1/z]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["ArcSec", "[", FractionBox["1", RowBox[List["1", "-", RowBox[List["2", SuperscriptBox["z", "2"]]]]]], "]"]], "\[Equal]", RowBox[List["2", " ", FractionBox[SqrtBox[SuperscriptBox["z", "2"]], "z"], RowBox[List["ArcCsc", "[", FractionBox["1", "z"], "]"]]]]]]]]

MathML Form

<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> <mfrac> <mn> 1 </mn> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </msqrt> </mrow> <mi> z </mi> </mfrac> <mo> ⁢ </mo> <mrow> <msup> <mi> csc </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arcsec /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <arccsc /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSec", "[", FractionBox["1", RowBox[List["1", "-", RowBox[List["2", " ", SuperscriptBox["z_", "2"]]]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", SqrtBox[SuperscriptBox["z", "2"]], " ", RowBox[List["ArcCsc", "[", FractionBox["1", "z"], "]"]]]], "z"]]]]]

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

2003-08-21