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http://functions.wolfram.com/01.11.33.0001.01
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Implies[Element[x, Rationals] && Element[Sec[x Degree], Rationals],
Sec[x] == 1 || Sec[x] == -1 || Sec[x] == 2 || Sec[x] == -2]
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Cell[BoxData[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["x", "\[Element]", "Rationals"]], "\[And]", RowBox[List[RowBox[List["Sec", "[", RowBox[List["x", " ", "Degree"]], "]"]], "\[Element]", "Rationals"]]]], ")"]], "\[Implies]", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Sec", "[", "x", "]"]], "\[Equal]", "1"]], "\[Or]", RowBox[List[RowBox[List["Sec", "[", "x", "]"]], "\[Equal]", RowBox[List["-", "1"]]]], "\[Or]", RowBox[List[RowBox[List["Sec", "[", "x", "]"]], "\[Equal]", "2"]], "\[Or]", RowBox[List[RowBox[List["Sec", "[", "x", "]"]], "\[Equal]", RowBox[List["-", "2"]]]]]], ")"]]]]]]
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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> <mo> ( </mo> <mrow> <mrow> <mi> x </mi> <mo> ∈ </mo> <semantics> <mi> ℚ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalQ]", Function[Rationals]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mi> sec </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> x </mi> <mo> ⁢ </mo> <mo> ° </mo> </mrow> <mo> ) </mo> </mrow> <mo> ∈ </mo> <semantics> <mi> ℚ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalQ]", Function[Rationals]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mrow> <mrow> <mi> sec </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mn> 1 </mn> </mrow> <mo> ∨ </mo> <mrow> <mrow> <mi> sec </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ∨ </mo> <mrow> <mrow> <mi> sec </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mn> 2 </mn> </mrow> <mo> ∨ </mo> <mrow> <mrow> <mi> sec </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <implies /> <apply> <and /> <apply> <in /> <ci> x </ci> <rationals /> </apply> <apply> <in /> <apply> <sec /> <apply> <times /> <ci> x </ci> <ci> Degree </ci> </apply> </apply> <rationals /> </apply> </apply> <apply> <or /> <apply> <eq /> <apply> <sec /> <ci> x </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <eq /> <apply> <sec /> <ci> x </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <eq /> <apply> <sec /> <ci> x </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <eq /> <apply> <sec /> <ci> x </ci> </apply> <cn type='integer'> -2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List["Implies", "[", RowBox[List[RowBox[List[RowBox[List["x", "\[Element]", "Rationals"]], "&&", RowBox[List[RowBox[List["Sec", "[", RowBox[List["x", " ", "\[Degree]"]], "]"]], "\[Element]", "Rationals"]]]], ",", RowBox[List[RowBox[List[RowBox[List["Sec", "[", "x", "]"]], "\[Equal]", "1"]], "||", RowBox[List[RowBox[List["Sec", "[", "x", "]"]], "\[Equal]", RowBox[List["-", "1"]]]], "||", RowBox[List[RowBox[List["Sec", "[", "x", "]"]], "\[Equal]", "2"]], "||", RowBox[List[RowBox[List["Sec", "[", "x", "]"]], "\[Equal]", RowBox[List["-", "2"]]]]]]]], "]"]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
