Pre Cal

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2cos*2x-cosx=1 find all solutions to the equation on the domain [0,2ð]

i got ð/4, 7ð/4, 3ð/4, and 5ð/4 but only got two out of four points... what did i do wrong?

  • Pre Cal -

    Is cos*2x supposed to mean cos^2 x?
    Is 2ð supposed to mean 2 pi?
    If so,
    2 cos^2x - cos x -1 = 0
    which factors into
    (2 cos x +1)(cos x -1) = 0
    The solutions occur where cos x = -1/2 or +1

    If cos*2x means cos(2x), then
    2[2 cos^2 x -1) - cos x -1 = 0
    4 cos^2 x -cos x -3 = 0
    (4 cosx +3)(cosx - 1) = 0
    x is where cos x = -3/4 or +1

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