mult the top and bottom by 1/tanx to get

there are a few ways to take this limit as x goes to zero the cool way is to expand cos as its power series

taking the limit as x goes to zero gives 1/2

or we could use L'hospitals rule

we have the zero over zero form taking the derivatives we get

use L.H again

taking the lim as x goes to zero gives 1/2 again.

Good luck.