Find the limit of lim (x --> 0) (tan(6t)) / sin(2t)
= sin 6t / cos 6t . 1/sin 2t = sin 6t / 6t . 6t/ sin 2t . 1/ cos 6t
=3 (sin 6t / 6t) . (2t/ sin 2t) . (1/ cos 6t)
As x → 0, the terms within the parentheses, each approach 1.
The limit is therefore = 3