without using mathematical table evaluate sin30-sin60/tan60

Answer 1

You must memorize the ratio of sides of the standard
30-60-90 ° triangle to be 1 : √3 : 2 respectively

then sin30° = 1/2
sin 60° = √3/2
tan 60° = √3/1 =√3

assuming you meant:
(sin30-sin60)/tan60
= (1/2 - √3/2)/√3
= (1/2 - √3/2)/√3* √3/√3
= (√3 - 3)/6

Answer 2

sin30 - sin60/tan60 = sin30 - cos60 = sin30 - sin30 = 0