Trigonometry

Solve the equation. (Find all solutions of the equation in the interval [0, 2π). Enter your answers as a comma-separated list.)
4 tan(2x) − 4 cot(x) = 0

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asked by Thomas
  1. tan(2x) = 2tanx/(1-tan^2 x)
    let tanx = k , then

    4 tan(2x) − 4 cot(x) = 0
    4(2k)/(1 - k^2) - 4/k = 0
    8k/(1 - k^2) = 4/k
    2k(1 - k^2) = 1/k
    2k^2 = 1 - k^2
    3k^2 = 1
    k = ±1/√3

    tanx = ±1/√3
    so x could be in any of the 4 quadrants,
    x = 30°, 150° , 210°, 330°
    or
    x = π/6, 5π/6, 7π/6, 11π/6

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    posted by Reiny
  2. I put that in and it said it wasn't correct. Is there anything that could be missing?

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    posted by Thomas
  3. well, π/6 works fine, since
    4(√3 - √3) = 0

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    posted by oobleck

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