Question

$tan{20}^0+tan{40}^0+..........+tan{180}^0=$

Answer 1

$=\tan 20+\tan 40+\tan 60+\tan 80+.....\tan 180$

$=\tan 20+\tan 40+\tan 60+\tan 80+\tan (180-100)+\tan (100-120)+\tan (100-140)+\tan (100-160)+\tan (100-180)$

$=\tan 20+\tan 40+\tan 60+\tan 80-\tan 20-\tan 40-\tan 60-\tan 80$

$=0$.