Trigonometry – How can I prevent Mathematica from simplifying basic trigonometric identities (1 / Cot (x))?

I am working on a code to display (Print ()) the answers of some exercises for my students. Some of the answers have parts like 1 / Cot (x). I want to prevent Mathematica from transforming this expression into Tan (x).

I tried (as another thread's suggestion)

Simplify(1/Cot(y), Trig -> False)

But it does not work. I also can't use Hold () because the expression refers to a previous calculation and I have to evaluate it. Advices ?? I have Mathematica 11.2 and forgive my English. Thank you!!