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 $\cot(x)= 1 \sqrt{2}$ 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). 
February 22nd, 2018, 03:48 AM  #5 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902  

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