How can this be solved?

Question

$3 {tan}^{3} x = tan x$ $3tan^3x = tanx$

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Answer 1 · 2018-02-25T01:15:53

See below.

$3 {tan}^{3} x = tan x \Rightarrow (3 {tan}^{2} - 1) tan x = 0$ $3tan^3x = tanx rArr (3tan^2-1)tanx=0$ After factoring, the conditions are:

${(tan^2 x= 1/3),(tanx=0):}$

and solving

$tan^2x = 1/3 rArr {(x = -pi/6 + k pi),(x=pi/6 + k pi):}$

$tanx = 0 rArr x = k pi$ , then the solutions are:

$x = {-pi/6 + k pi}uu{pi/6 + k pi}uu { k pi}$ for $k in ZZ$

I hope that helps!

Answer 2 · 2018-02-25T23:24:01

See below.

Here is the solution process for the above equation:

$3tan^3x=tanx$

$3tan^3x-tanx=0$

$tanx(3tan^2x-1)=0$

$tanx=0$ and $3tan^2x-1=0$

$x=pi/4 " or " (3pi)/4 or pi/6 or (7pi)/6$

I hope that helps!