My Math Forum equation

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 February 21st, 2018, 07:41 AM #1 Newbie   Joined: Feb 2018 From: Slovakia Posts: 2 Thanks: 0 equation Could you please help me with this equation? I got stuck :/ (cos(x)-sin(x))^2=2(sin(x))^2
 February 21st, 2018, 08:18 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 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 $\cot(x)= 1- \sqrt{2}$ Thanks from topsquark Last edited by skipjack; February 21st, 2018 at 10:49 AM.
 February 21st, 2018, 08:56 AM #3 Newbie   Joined: Feb 2018 From: Slovakia Posts: 2 Thanks: 0 I don't get 2 last rows. Last edited by skipjack; February 21st, 2018 at 10:49 AM.
 February 21st, 2018, 11:06 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,757 Thanks: 2138 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). Thanks from greg1313 and topsquark
February 22nd, 2018, 03:48 AM   #5
Math Team

Joined: Jan 2015
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Quote:
 Originally Posted by sima I don't get 2 last rows.
$cot(x)= \frac{cos(x)}{sin(x)}$.

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