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February 21st, 2018, 07:41 AM   #1
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equation

Could you please help me with this equation? I got stuck :/
(cos(x)-sin(x))^2=2(sin(x))^2
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February 21st, 2018, 08:18 AM   #2
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The first thing I would do is take the square root of both sides:
$\cos(x)- \sin(x)= \pm\sqrt{2}\sin(x)$

We can divide that into two equations,
$\cos(x)- \sin(x)= \sqrt{2}\sin(x)$ so that
$\cos(x)= (1+ \sqrt{2})\sin(x)$ and
$\cot(x)= 1+ \sqrt{2}$

and
$\cos(x)- \sin(x)= -\sqrt{2}\sin(x)$ so that
$\cos(x)= (1- \sqrt{2})\sin(x)$ and
$\cot(x)= 1- \sqrt{2}$
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Last edited by skipjack; February 21st, 2018 at 10:49 AM.
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February 21st, 2018, 08:56 AM   #3
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I don't get 2 last rows.

Last edited by skipjack; February 21st, 2018 at 10:49 AM.
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February 21st, 2018, 11:06 AM   #4
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cos²(x) + sin²(x) - 2sin(x)cos(x) = 2sin²(x)
sin(2x) = 1 - 2sin²(x) = cos(2x)
tan(2x) = 1
2x = $\pi$/4 + k$\pi$, where k is an integer
x = $\pi$/8 + k$\pi$/2 (or (4k + 1)$\pi$/8 if you prefer).
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February 22nd, 2018, 03:48 AM   #5
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Quote:
Originally Posted by sima View Post
I don't get 2 last rows.
$cot(x)= \frac{cos(x)}{sin(x)}$.
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