We have been given a trigonometric function and we need to determine its vertical asymptotes.
We have, [tex]h(x)=\frac{cos(x)}{sin(2x)}[/tex]
We can find its vertical asymptotes by setting the denominator equal to zero.
[tex]sin(2x)=0\\ 2x=n\pi \\ \\ x=\frac{n\pi}{2}[/tex]
Therefore, vertical asymptotes of the given function occur at [tex]x=\frac{n\pi}{2}[/tex], Where n is any integer.