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Solve cos(2x) = cos(x) for 0 <= x <= 2*pi.

 Jun 9, 2020
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cos (2x) = cos^2 - sin^2     or      2 cos^2 x -1

 

 

sooo   2 cos^2 x  -1 = cos x

       

          2 cos^2 x - cos x - 1 = 0        let    x = cos x       then use quadratic formula to find x = 1 or - 1/2

 

cos x = 1 or -1/2     then from 0 to 2pi    this is      0    2 pi      and      2pi/3    4pi/3  

 Jun 9, 2020

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