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MATH C30

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Solve cosxtanx + sqroot3cosx - sqroot3/2tanx - 3/2 = 0
interval 0 to 2 pi
exact answers and formula for the general solution as well as the specific solutions.

Sorry Steve, missed it last night.

  • MATH C30 -

    If I'm reading it right, we have

    cos tan + √3 cos - √3/2 tan - 3/2 = 0

    rearrange terms a bit to get

    tan(cos - √3/2) + √3(cos - √3/2) = 0
    (tan + √3)(cos - √3/2) = 0

    tan x = -√3 --> x = 2pi/3 or 4pi/3
    x = (2k+1)*pi +/- pi/3

    cos x = √3/2 --> x = pi/6 or 11pi/6
    x = k*2pi +/- pi/6

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