# What are the asymptote(s) and hole(s), if any, of  f(x) =tan(pi+x)*cos(pi/12+x) /(x-(11pi)/12) ?

There is a vertical Asymptote $x - \left(11 \frac{\pi}{12}\right)$=0 or $x = \frac{11 \pi}{12}$and also asymptotes $x = \pm \frac{\pi}{2} , \pm 3 \frac{\pi}{2.} .$
There is a vertical Asymptote $x - \left(11 \frac{\pi}{12}\right)$=0 or $x = \frac{11 \pi}{12}$and also asymptotes $x = \pm \frac{\pi}{2} , \pm 3 \frac{\pi}{2.} .$