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Solve for all real values of x.

3tan^2x = 3^1/2 tan x

I have no idea how to approach this problem.

  • calculus -

    3^1/2 tan x *(3^1/2*tanx - 1)= 0
    tan x = 0 or 1/sqrt3

    x = 0, pi, pi/6 and one other tan^-1(1/sqrt3)

  • calculus -

    3tan^2x = 3^1/2 tan x
    3tan^2x - √3tan x = 0
    tanx(3tanx - √3) = 0
    so tanx = 0 or tanx = √3/3

    if tanx = 0, then x = 0º, 180º, 360º, ...
    if tanx = √3/3 then x = 30º, 210º,390º, ...

    The period of the tangent function is 180º, so adding 180 to any of our answers produces more answers

    the angles in radians would be
    0, pi, 2pi ...
    pi/6, 7pi/6, 13pi/6, ..
    (adding pi each time)

  • calculus -

    Much appreciated guys.

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