SOLUTION: Solve the equation on the interval [0,2pi] sqrt(3) tan^2 x = 3 tan x

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Question 1121660: Solve the equation on the interval [0,2pi]
sqrt(3) tan^2 x = 3 tan x
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!


This is true if either:

And ,
Also



Answer by ikleyn(52864)   (Show Source): You can put this solution on YOUR website!
.

The solution by @josmiceli was partly incomplete and partly incorrect - so I put my solution below. 


 tan^2  x =   ====>   divide both sides by   ====>


tan^2(x) = 


 = 0


 = 0


This equation deploys in two separate equations:


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


and


    2)  tan(x) = ,  which also has two solutions in the given interval  x=   and  x= .


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


                0,  ,    and  .

Solved.


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