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 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: 20,942 Thanks: 2210 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). Thanks from topsquark
 February 28th, 2018, 11:30 PM #3 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond $$\cos(x)-\sin(x)-\cos(3x)+\sin(3x)$$ $$\cos(x)-\sin(x)-4\cos^3(x)+3\cos(x)+3\sin(x)-4\sin^3(x)$$ $$4\cos(x)-4\cos^3(x)+2\sin(x)-4\sin^3(x)$$ $$4\cos(x)(1-\cos^2(x))+2\sin(x)(1-2\sin^2(x))$$ $$4\cos(x)\sin^2(x)+2\sin(x)\cos(2x)$$ $$2\sin(x)\sin(2x)+2\sin(x)\cos(2x)$$ $$...$$

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