marasofia1616
Find all solutions to the equation in the interval [0, 2π).
cos 2x  cos x = 0



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hieuvo
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so, cos2x=cosx, I think x is in those special angles

RadEn
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use identity : cos2x=2cos^2 x  1

RadEn
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so, we have a quadratic equation in form cosx,
2cos^2 x  1  cosx = 0 or
2cos^2 x  cosx  1 = 0
can u factor out it

marasofia1616
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ok I get cos x(2 cos x1)=1

RadEn
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np, it should be
(2cosx + 1)(cosx  1) = 0

RadEn
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now, for zeroes take each factors be zero, so
2cosx+1=0 or cosx1=0
solve for x

marasofia1616
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ok I got the solutions 0, 2pi/3 and 4pi/3

marasofia1616
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thank you

RadEn
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but, i miss one root :)

RadEn
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looks 0 be same for 2pi, right ?

marasofia1616
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I got the answer right

RadEn
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ok, great..