How do you solve $3tan^2x=sqrt3tanx$ ?

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Answer 1 · 2017-02-09T03:17:32

$x= 0, pi/6, pi, (7pi)/6$

Solve for $tan x$ ,
$3 tan^2 x -sqrt3 tan x =0$

$sqrt3 tan x (sqrt3 tan x -1)=0$

Thus $tan x=0, tanx = 1/sqrt3$

For tan x =0, the principal solution is $x=0, pi$

For $tan x= 1/sqrt3$ , the principal solution would be $x= pi/6, (7pi)/6$

How do you solve 3tan^2x=sqrt3tanx3tan^2x=sqrt3tanx?