Demonstration.  Establish the identity  [Graphics:Images/ComplexFunTrigMod_gr_115.gif].  

Exploration Method (ii).

Use Mathematica's "ComplexExpand" procedure.

[Graphics:../Images/ComplexFunTrigMod_gr_121.gif]

[Graphics:../Images/ComplexFunTrigMod_gr_122.gif]

[Graphics:../Images/ComplexFunTrigMod_gr_123.gif]

Therefore,  [Graphics:../Images/ComplexFunTrigMod_gr_124.gif].  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2006 John H. Mathews, Russell W. Howell