Question

Тригонометрия: tg^3(x)-tg(x)=0

Answer 1

tgx(tg²x-1)=0
tgx=0⇒x=πn
tg²x=1
tgx=1⇒x=π/4+πn
tgx=-1⇒x=-π/4+πn

Answer 2

$tg^3x-tgx=0 \\ tgx~(tg^2x-1)=0 \\ \\ 1)~tgx=0 \\ ~~~~~x= \pi k \\ \\ 2)~tg^2x-1=0 \\ ~~~~~tg^2x=1 \\ ~~~~tgx=б1 \\ ~~~~x=б \frac{ \pi }{4} + \pi k$

Ответ:  $\pi k;~~б\frac{ \pi }{4} + \pi k$