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March 27, 2017

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cos^2x-sin^2 x+1=cos x

  • pre-calc help !!!!!!! - ,

    sin^2 x = 1 - cos^2 x

    so we have
    cos^2 x - 1 + cos^2 x + 1
    or
    2 cos^2 x
    on the left
    so

    2 cos^2 x = cos x

    cos x = 1/2

    x = 60 degrees or pi/3 radians
    or
    300 degrees or 5 pi/3 radians

  • pre-calc help !!!!!!! - ,

    from Damon's middle section:

    2cos^2 x - cosx = 0
    cosx(2cosx - 1) = 0
    cosx = 0 or cosx = 1/2
    so from cosx=1/2 we have the 2 answers that Damon gave

    from cosx = 0 , we also have
    x = 90° or x = 270°
    x = π/2 or x = 3π/2

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