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August 6th, 2013, 04:25 AM  #1 
Senior Member Joined: Sep 2010 From: Oslo, Norway Posts: 162 Thanks: 2  Express cos(4a) + sin(4a) using only cos(a) and sin(a)
Hello, Distribute and group terms containing i: 1. Now, just by seeing a glaring pattern, I am almost convinced that and , but how can I be sure? 2. What is the name of the "method" used to arrive at the above conclusion? (I am sorry that I do not know a more precise word than 'method'.) Thank you for your time. Kind regards, Marius 
August 6th, 2013, 01:01 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,770 Thanks: 700  Re: Express cos(4a) + sin(4a) using only cos(a) and sin(a)
1. When you have an equation involving complex quantities, the real and imaginary parts are separate equations. 2. I don't know if it has a specific name. Question  title seems to have little relation to the text. 
September 6th, 2013, 01:48 AM  #3 
Newbie Joined: Jun 2013 Posts: 15 Thanks: 0  Re: Express cos(4a) + sin(4a) using only cos(a) and sin(a)
Hi solved your problem here "Solution: Given cos (3?) + i sin (3?) = (cos ? + i sin ?)^3 we know by de Moivre's theorem (cos ? + i sin ?)^n = cos (n?) + i sin (n?) where cos (3?) = cos^3 ?  3cos ? sin² ? sin (3?) = 3cos² ?  sin ^3 ? " 
September 6th, 2013, 12:09 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,757 Thanks: 2138 
Similarly, cos(4a) + sin(4a) ? 1 + 4sin(a)cos³a  8sin²a cos²a  4sin³a cos(a).


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