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Answer 1 · 2017-03-23T20:48:43

$x={0,pi/4,3/4pi,pi,5/4pi,7/4pi,2pi}$

$tan^8 x -tan^4 x=tan^4x(tan^4x-1)=0$

so we have

$tan^4 x=0->tan x = 0$

and

$tan^4x-1=(tan^2x+1)(tan^2x-1)=(tan^2x+1)(tanx-1)(tanx+1)$

Here $tan^2x+1=0$ is unfeasible so we will consider only

${(tanx=0),(tanx=1),(tanx=-1):}$

and then

$x = kpi uu x=pi/4+kpiuux=3/4pi+kpi$ for $k=0,1,2,cdots$

or

$x={0,pi/4,3/4pi,pi,5/4pi,7/4pi,2pi}$