Докажите тождество tgα+tgβ tg (α+β)=_________ 1-tgαtgβ

tg (α+β)=sin (α+β) / cos (α+β)=(sin α*cos β+cos α*sin β) / (cos α*cos β — sin α*sin β)=(sin α*cos β+cos α*sin β) / (cos α*cos β) / (cos α*cos β — sin α*sin β) / (cos α*cos β)=(tg α+tg β) / (1 — tg α*tg β)