Sec[a] Csc[b] == 2/(Sin[a + b] - Sin[a - b])

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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> <mi> sec </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> csc </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mfrac> <mn> 2 </mn> <mrow> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <sec /> <ci> a </ci> </apply> <apply> <csc /> <ci> b </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <apply> <sin /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <sin /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Sec", "[", "a_", "]"]], " ", RowBox[List["Csc", "[", "b_", "]"]]]], "]"]], "\[RuleDelayed]", FractionBox["2", RowBox[List[RowBox[List["Sin", "[", RowBox[List["a", "+", "b"]], "]"]], "-", RowBox[List["Sin", "[", RowBox[List["a", "-", "b"]], "]"]]]]]]]]]

2003-08-21