How can this be solved?

Question

#3tan^3x = tanx#

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Answer 1 · 2018-02-25T01:15:53

See below.

#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!