Question

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

Answer 1

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

Explanation:

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`