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 August 27th, 2016, 04:22 PM #1 Newbie   Joined: Aug 2016 From: Brazil Posts: 8 Thanks: 0 indicate least positive angle Indicate the smallest positive angle that verifies the equation $\displaystyle \cos(\frac{x}{4}) + \cos(\frac{x}{5}) + 3\cos(\frac{x}{10}) + 3\cos\frac{x}{20}=0$ ANSWER $\displaystyle \frac{20\pi}{3}$ Thank You Last edited by skipjack; August 28th, 2016 at 01:56 AM. August 28th, 2016, 12:33 AM #2 Newbie   Joined: Dec 2006 Posts: 5 Thanks: 2 Transform the sums in products using the formula $\displaystyle \cos a+\cos b=2\cos\frac{a+b}{2}\cos\frac{a-b}{2}$ and we have $\displaystyle 2\cos\frac{9x}{40}\cos\frac{x}{40}+6\cos\frac{3x}{ 40}\cos\frac{x}{40}=0$ $\displaystyle 2\cos\frac{x}{40}\left(\cos\frac{9x}{40}+ 3\cos\frac{3x}{40}\right)=0$ Then $\displaystyle \cos\frac{x}{40}=0\Rightarrow x=20\pi$ or $\displaystyle \cos\frac{9x}{40}+3\cos\frac{3x}{40}=0$ Now we use the formula $\displaystyle \cos 3a=4\cos^3a-3\cos a$ and the equation becomes $\displaystyle 4\cos^3\frac{3x}{40}=0\Rightarrow \frac{3x}{40}=\frac{\pi}{2}\Rightarrow x=\frac{20\pi}{3}$ Thanks from Nathalia Last edited by skipjack; August 28th, 2016 at 01:58 AM. Tags angle, positive 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 GIjoefan1976 Algebra 4 February 16th, 2016 12:55 PM randomgamernerd Geometry 2 November 17th, 2015 08:03 AM Tangeton Trigonometry 4 January 9th, 2015 03:13 AM Gyiove Algebra 1 February 26th, 2014 04:57 PM kingkos Algebra 2 December 7th, 2012 05:34 PM

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