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 August 27th, 2016, 04:14 PM #1 Newbie   Joined: Aug 2016 From: Brazil Posts: 8 Thanks: 0 indicate first three positive solutions Solve $\displaystyle \tan(3x) + \cot(x) = \tan(x) + \cot(3x)$. Indicate first three positive solutions. Answer: $\displaystyle \frac{\pi }{4},\frac{3 \pi}{4},\frac{5 \pi}{4}$ Last edited by skipjack; August 28th, 2016 at 02:01 AM. August 28th, 2016, 12:47 AM #2 Newbie   Joined: Dec 2006 Posts: 5 Thanks: 2 $\displaystyle \tan 3x-\tan x=\cot 3x-\cot x$ $\displaystyle \frac{\sin 2x}{\cos x\cos 3x}=-\frac{\sin 2x}{\sin x\sin 3x}$ $\displaystyle \sin 2x(\cos x\cos 3x+\sin x\sin 3x)=\Rightarrow \sin 2x\cos 2x=0$ Multiply both members by 2 $\displaystyle \sin 4x=0\Rightarrow x=\frac{k\pi}{4}$ The first three positive solutions are obtained for $\displaystyle k=1, \ 3, \ 5$ Thanks from Nathalia Tags positive, solutions 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 mandradebs Number Theory 2 October 19th, 2014 07:43 AM mared Algebra 3 April 7th, 2014 04:07 PM ducnhuandoan Number Theory 4 May 1st, 2012 04:46 AM pesius Linear Algebra 1 March 28th, 2011 03:22 PM nooblet Number Theory 4 March 18th, 2009 08:34 PM

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