Precalculus

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Solve Cos^2(x)+cos(x)=cos(2x). Give exact answers within the interval [0,2π)

Ive got the equation down to -cos^2(x)+cos(x)+1=0 or and it can be simplified too sin^2(x)+cos(x)=0
If you could tell me where to go from either of these two, it would be great help.. Thankyou for any responses

  • Precalculus -

    cos^2(x) + cos(x) = 2cos^2(x) - 1
    cos^2(x) - cos(x) - 1 = 0
    This is just like

    u^2 - u - 1 = 0
    u = [1 +/- sqrt(5)]/2

    since u = cos(x) and must be less than 1,

    cos(x) = (1-sqrt(5))/2
    will be in QII or QIII

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