√3 cosec 20° - sec 20°
= √3 . 1/sin 20° - 1/cos 20°
= (√3 . cos 20° - 1 . sin 20°)/(sin 20° . cos 20°) . 4/4
= 4 ((1/2 .√3) cos 20° - (1/2) . sin 20°)/(2 . sin 20° cos 20°)
= 4 (sin 60° cos 20° - cos 60° . sin 20°)/(sin (2 . 20°)
= 4 (sin (60 - 20)°)/sin 40°
= 4 . sin 40° / sin 40°
= 4