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Forum Index -> Trignometry like the article? email it to a friend.  
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[Post New]19 Apr 2008 10:04:35 IST
    Subject: problem
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nics (166)

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8 power 1+ mod cos x +cos square x +mod cos x whole cube +.......upto infinity = 4 power 3 . find the general solution
 
    
[Post New]19 Apr 2008 12:14:03 IST
    Subject: Re:problem
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sboosy (3011)

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8^{1+|\cos(x)|+|\cos^2(x)|+|\cos^3(x)|+....} = 4^3 = 2^6 \\ \\ 8^{\frac{1}{1-|\cos(x)|}} = 2^6 \\ \\ \Rightarrow 2^{\frac{3}{1-|\cos(x)|}}=2^6 \\ \\ \Rightarrow 1-|\cos(x)| = \frac{1}{2} \\ \\ \Rightarrow |\cos(x)| = \frac{1}{2} \\ \\ \Rightarrow \cos(x) = \pm \frac{1}{2} \\ \\ \cos(x) = \frac{1}{2} \ \Rightarrow x=2n\pi \pm \frac{\pi}{3} \\ \\ \cos(x) = \frac{-1}{2} \ \Rightarrow x = 2n\pi \pm \frac{2\pi}{3} \\ \\ \mbox{Their union is the general solution}
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