Infinite continued fraction implies that the number is irrational

Question

I've read recently that any number with infinite continued fraction is irrational. See this continued fraction below

https://www.wolframalpha.com/input/?i=continued+fraction+of+the+cosine If I substitute x for $\frac{\pi}{2}$ I will get zero on the left side, but the continued fraction is infinite because its convergent ones never cancel out. Could anyone explain me this?

Answer 1

Answered (in general) by @bof in a comment:

[...] a number with an infinite simple continued fraction expansion is irrational. A continued fraction is "simple" if all the partial numerators are ones.