Is it worth it taking these two classes together?Or does precalc cover most topics from trig?
PreCalc includes Trig but Trig does not include PreCalc.
PreCalc is pretty much Trig + Other random stuffs that’s not useful for Calculus but could be useful for Linear Algebra
(basic matrices, etc.)
So, no, you should not be taking 2 of those classes together because 1 has all of the other.
Think of Trig as… hmm, what’s a good analogy:
If you are learning all about quadrilaterals (= PreCalc), then Trig is squares.
Since you are learning all about quadrilaterals, by default, you should come to understand all of Trig.
So…
moral of story is:
Take PreCalc only. 
You need to check the course descriptions for your school. I’ve never seen trigonometry offered on its own, and it’s possible that the pre-calculus class doesn’t cover it. (Sometimes trigonometry is part of Algebra II rather than pre-calculus.)