Sin[a Sqrt[b z^2]] == (Sqrt[b z^2]/(Sqrt[b] z)) Sin[a Sqrt[b] z]

Cell[BoxData[RowBox[List[RowBox[List["Sin", "[", RowBox[List["a", " ", SqrtBox[RowBox[List["b", " ", SuperscriptBox["z", "2"]]]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[SqrtBox[RowBox[List["b", " ", SuperscriptBox["z", "2"]]]], RowBox[List[SqrtBox["b"], " ", "z"]]], RowBox[List["Sin", "[", RowBox[List["a", " ", SqrtBox["b"], " ", "z"]], "]"]]]]]]]]

<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> &#8290; </mo> <msqrt> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <msqrt> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mrow> <msqrt> <mi> b </mi> </msqrt> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msqrt> <mi> b </mi> </msqrt> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sin /> <apply> <times /> <ci> a </ci> <apply> <power /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sin /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sin", "[", RowBox[List["a_", " ", SqrtBox[RowBox[List["b_", " ", SuperscriptBox["z_", "2"]]]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox[RowBox[List["b", " ", SuperscriptBox["z", "2"]]]], " ", RowBox[List["Sin", "[", RowBox[List["a", " ", SqrtBox["b"], " ", "z"]], "]"]]]], RowBox[List[SqrtBox["b"], " ", "z"]]]]]]]

2007-05-02