February 28th, 2018, 01:16 AM  #1 
Newbie Joined: Feb 2018 From: Belgium Posts: 1 Thanks: 0  Simplify
Hello, I can’t simplify this equation. I already tried to solve it. cos x  sin x  cos3x + sin3x/sin2x + cos2x Last edited by skipjack; February 28th, 2018 at 06:53 AM. 
February 28th, 2018, 07:01 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,961 Thanks: 1605 
I assume you meant the expression (cos(x)  sin(x)  cos(3x) + sin(3x))/(sin(2x) + cos(2x)). As cos(x)  cos(3x) = 2sin(x)sin(2x) and sin(3x)  sin(x) = 2cos(2x)sin(x), (cos(x)  sin(x)  cos(3x) + sin(3x))/(sin(2x) + cos(2x)) = (2sin(x)(sin(2x) + cos(2x)))/(sin(2x) + cos(2x)) = 2sin(x). 
February 28th, 2018, 11:30 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,807 Thanks: 1045 Math Focus: Elementary mathematics and beyond 
$$\cos(x)\sin(x)\cos(3x)+\sin(3x)$$ $$\cos(x)\sin(x)4\cos^3(x)+3\cos(x)+3\sin(x)4\sin^3(x)$$ $$4\cos(x)4\cos^3(x)+2\sin(x)4\sin^3(x)$$ $$4\cos(x)(1\cos^2(x))+2\sin(x)(12\sin^2(x))$$ $$4\cos(x)\sin^2(x)+2\sin(x)\cos(2x)$$ $$2\sin(x)\sin(2x)+2\sin(x)\cos(2x)$$ $$...$$ 

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