Question 1078893
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Find all solutions of the equation in the interval [0, 2π). 
9 tan ^3 x = 3 tan x
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{{{9*tan^3(x)}}} = {{{3*tan(x)}}}  --->  

{{{9*tan^3(x) - 3*tan(x)}}} = {{{0}}}  --->  Factor the left side

{{{3*tan(x)*(3*tan^2(x)-1)}}} = {{{0}}}


This equation deploys in two independent equations


1.  tan(x) = 0  with the solutions  x = {{{0}}} and x = {{{pi}}} in the given interval.


2.  3*tan^2(x) - 1 = 0   <---->  {{{tan^2(x)}}} = {{{1/3}}}  ---->  tan(x) = +/-{{{sqrt(3)/3}}},  which has four solutions in the given interval

    x = {{{pi/6}}},  x = {{{5pi/6}}},  x = {{{7pi/6}}}  and  x = {{{11pi/6}}}.


<U>Answer</U>.  The given equation has 6 solutions in the given interval:

         x = 0, x = x = {{{pi/6}}},  x = {{{5pi/6}},  x = {{{pi}}},  x = {{{7pi/6}}}  and  x = {{{11pi/6}}}.
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