Формула  тангенса разности двух углов :

[tex]\displaystyle\bf\\\boxed{tg(x-y)=\frac{tgx-tgy}{1+tgx\cdot tgy} }\\\\\\\\\frac{tg340^\circ-tg100^\circ}{1+tg340^\circ\cdot tg100^\circ} =tg(340^\circ-100^\circ)=tg240^\circ=\\\\\\=tg(180^\circ+60^\circ)=tg60^\circ=\sqrt{3}[/tex]