My Math Forum indicate first three positive solutions

 Trigonometry Trigonometry Math Forum

 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 Display Modes Linear 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

 Contact - Home - Forums - Cryptocurrency Forum - Top