Question 1121755
.
<pre>
{{{sqrt(3)}}} tan^2  x = {{{3tanx}}}  ====>   divide both sides by {{{sqrt(3)}}}  ====>


tan^2(x) = {{{sqrt(3)*tan(x)}}}


{{{tan^2(x) - sqrt(3)*tan(x)}}} = 0


{{{tan(x)*(tan(x) - sqrt(3))}}} = 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(3)}}},  which also has two solutions in the given interval  x= {{{pi/3}}}  and  x= {{{4pi/3}}}.


<U>Answer</U>.  The original equation has 4 solutions in the given interval:


                0,  {{{pi}}},  {{{pi/3}}}  and  {{{4pi/3}}}.
</pre>

Solved.