What is trans-addition? A question from JEE-Advanced(2017) :
 

Bromination of both Z-but-2ene and E-but-2-ene involve syn and anti addition. So, there would be 4 products as suggested in the question. But, I don't understand the terminology of 'trans-addition', mentioned in the question.

What is actually trans addition?
Just like @QuantumAMERICCINO has pointed out, it's probably anti addition.

Furthermore, you seem to wonder why a syn compound doesn't form. It all lies in the mechanism of bromination:

The double bond in cis-2-butene polarises the $\ce{Br-Br}$ bond in a nearby $\ce{Br2}$ molecule. A $\ce{Br+}$ ion attacks the double bond and forms a bromonium ion.



The bromonium ion makes the adjacent carbon atoms electrophilic. The bromide may attack the most electrophilic out of them. Here, however, they are equivalent.



You should now be able to understand how the mechanism works.