SOLUTION: Solve the equation on the interval [0, 2pi) {{{sqrt(3)}}} tan^2 x = {{{3tanx}}} Can i get everything on one side and factor? I知 not sure what the [0,2pi) means for restrict

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the equation on the interval [0, 2pi) {{{sqrt(3)}}} tan^2 x = {{{3tanx}}} Can i get everything on one side and factor? I知 not sure what the [0,2pi) means for restrict      Log On


   

Question 1121755: Solve the equation on the interval [0, 2pi)
sqrt%283%29 tan^2 x = 3tanx
Can i get everything on one side and factor? I知 not sure what the [0,2pi) means for restrictions.
Answer by ikleyn(52807) About Me  (Show Source):
You can put this solution on YOUR website!
.
sqrt%283%29 tan^2  x = 3tanx  ====>   divide both sides by sqrt%283%29  ====>


tan^2(x) = sqrt%283%29%2Atan%28x%29


tan%5E2%28x%29+-+sqrt%283%29%2Atan%28x%29 = 0


tan%28x%29%2A%28tan%28x%29+-+sqrt%283%29%29 = 0


This equation deploys in two separate equations:


    1)  tan(x) = 0,  which has two solutions in the given interval:  x= 0  and  x= pi;


and


    2)  tan(x) = sqrt%283%29,  which also has two solutions in the given interval  x= pi%2F3  and  x= 4pi%2F3.


Answer.  The original equation has 4 solutions in the given interval:


                0,  pi,  pi%2F3  and  4pi%2F3.

Solved.