Question

Помогите!!!!срочно!!!!
$tgxtg20+tg20tg40+tg40tgx=1$

Answer 1

tg(x)=( 1-tg(20)*tg(40) ) / ( tg(20) + tg(40) ) = 1/tg(20+40) = 1/tg(60) = 1/корень(3)
х = 30 + pi*k

Answer 2

tgxtg20+tgxtg40=1-tg20tg40
tgx(tg20+tg40)=1-tg20tg40
tgx=(1-tg20tg40)/(tg20+tg40)
tg(a+b)=(tga+tgb)/(1-tgatgb)⇒1/tg(a+b)=(1-tgatgb)/(tga+tgb)⇒
tgx=1/tg(20+40)=1/tg60=1/√3
x=π/6+πn