Trigonometry Trigonometry Math Forum

 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

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Quote:
 Originally Posted by sima I don't get 2 last rows. $cot(x)= \frac{cos(x)}{sin(x)}$. Tags equation Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post max233 Algebra 2 March 31st, 2017 09:40 PM shaharhada Algebra 2 August 30th, 2016 11:09 AM DarkX132 Algebra 3 September 26th, 2014 10:15 PM Sonprelis Calculus 6 August 6th, 2014 10:07 AM PhizKid Differential Equations 0 February 24th, 2013 10:30 AM

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