Osborn's Rule

Author

Eric W. Weisstein
March 25, 2009

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Trigonometry/OsbornsRule.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/OsbornsRule.html.

©2009 Wolfram Research, Inc. except for portions noted otherwise

Examples

#==TrigExpand[#]&/@Flatten[Outer[#1[x+#2 y]&,{Cos,Sin},{-1,1}]]

#==TrigExpand[#]&/@Flatten[Outer[#1[x+#2 y]&,{Cosh,Sinh},{-1,1}]]

#==TrigExpand[#]&/@Flatten[Outer[#1[x+#2 y]&,{Cos,Sin},{-1,1}]]/.{Cos->Cosh,Sin->Sinh}/.{Sinh[x]Sinh[y]:>-Sinh[x]Sinh[y]}