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February 28th, 2018, 01:16 AM   #1
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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.
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February 28th, 2018, 07:01 AM   #2
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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).
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February 28th, 2018, 11:30 PM   #3
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$$\cos(x)-\sin(x)-\cos(3x)+\sin(3x)$$

$$\cos(x)-\sin(x)-4\cos^3(x)+3\cos(x)+3\sin(x)-4\sin^3(x)$$

$$4\cos(x)-4\cos^3(x)+2\sin(x)-4\sin^3(x)$$

$$4\cos(x)(1-\cos^2(x))+2\sin(x)(1-2\sin^2(x))$$

$$4\cos(x)\sin^2(x)+2\sin(x)\cos(2x)$$

$$2\sin(x)\sin(2x)+2\sin(x)\cos(2x)$$

$$...$$
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