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http://functions.wolfram.com/01.12.16.0008.01
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ArcSin[Sqrt[(z - 1)/z]] == Pi/2 - ArcSin[1/Sqrt[z]] /; Abs[Arg[z]] < Pi
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSin", "[", SqrtBox[FractionBox[RowBox[List["z", "-", "1"]], "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["\[Pi]", "2"], "-", " ", RowBox[List["ArcSin", "[", FractionBox["1", SqrtBox["z"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", "z", "]"]], "]"]], "<", "\[Pi]"]]]]]]
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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> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mfrac> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mi> z </mi> </mfrac> </msqrt> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> <mo> - </mo> <mtext> </mtext> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mn> 1 </mn> <msqrt> <mi> z </mi> </msqrt> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mo> < </mo> <mi> π </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <arcsin /> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <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> <apply> <arcsin /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <lt /> <apply> <abs /> <apply> <arg /> <ci> z </ci> </apply> </apply> <pi /> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", SqrtBox[FractionBox[RowBox[List["z_", "-", "1"]], "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List["ArcSin", "[", FractionBox["1", SqrtBox["z"]], "]"]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", "z", "]"]], "]"]], "<", "\[Pi]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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