September 16th, 2009, 09:49 AM  #1 
Newbie Joined: Sep 2009 Posts: 3 Thanks: 0  trigonometry
Write 2sin²5xcos3x as a sum of cosinus and/or sinusterms. Use Eulers formula if you can. Also control your answer by putting x=0 before and after. I can't even start with x=0 in this one is it 2sin²5*0cos3*0 = 0 ? Please show me every step in how you do it, because this is the hardest thing to me to understand. 
September 16th, 2009, 04:42 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 716  Re: trigonometry
For your last question, sinx = 0 when x = 0. So any expression multiplied by sinax, where a is any constant, will be 0.

September 17th, 2009, 03:01 AM  #3 
Newbie Joined: Sep 2009 Posts: 3 Thanks: 0  Re: trigonometry
well, certainly doesn't help me much though Doesn't even know how to start, should i rewrite the cosinepart of the equation, or sine? And how? 
September 17th, 2009, 05:25 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,931 Thanks: 2205 
One way to do it is to replace 2sin²(5x) with 1  cos(10x). That gives you (1  cos(10x))cos(3x), i.e., cos(3x)  cos(10x)cos(3x). Now cos(10x)cos(3x) can be replaced with (cos(13x) + cos(7x))/2. 
September 17th, 2009, 07:37 AM  #5 
Newbie Joined: Sep 2009 Posts: 3 Thanks: 0  Re: trigonometry
Solved it, and controlled my answer with yours to be sure. This looks right? 
September 18th, 2009, 07:17 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,931 Thanks: 2205 
Yes, but omit the redundant "=" at the end of a line when the next line starts with "=".


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