Sin[a + b] == Sin[a] Cos[b] + Cos[a] Sin[b]

Cell[BoxData[RowBox[List[RowBox[List["Sin", "[", RowBox[List["a", "+", "b"]], "]"]], "\[Equal]", " ", RowBox[List[RowBox[List["Sin", "[", "a", "]"]], RowBox[List["Cos", "[", "b", "]"]]]], "+", RowBox[List[RowBox[List["Cos", "[", "a", "]"]], " ", RowBox[List["Sin", "[", "b", "]"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sin /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <sin /> <ci> a </ci> </apply> <apply> <cos /> <ci> b </ci> </apply> </apply> <apply> <times /> <apply> <cos /> <ci> a </ci> </apply> <apply> <sin /> <ci> b </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sin", "[", RowBox[List["a_", "+", "b_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Sin", "[", "a", "]"]], " ", RowBox[List["Cos", "[", "b", "]"]]]], "+", RowBox[List[RowBox[List["Cos", "[", "a", "]"]], " ", RowBox[List["Sin", "[", "b", "]"]]]]]]]]]]

2001-10-29