# For what values of x, if any, does f(x) = cot(pi/8-2x)  have vertical asymptotes?

f(x)=cot(π/8-2x) =cos(π/8-2x)/sin(π/8-2x)
sin(π/8-2x) = 0 <=> π/8-2x=kπ , $k$$\in \mathbb{Z}$
You can find some by replacing for $k = 1$ , $k = 2$ ,... $k = n$ and solving as $x$