Question

What are the asymptotes for `f(x) = tan(2x)`?

Answer 1

Note that `tan(2x)=sin(2x)/cos(2x)`.

This expression will form asymptotes when `cos(2x)=0`.

This expression is zero when `2x=+-(n+1/2)pi, n=0,1,2...`.

Therefore the asymptotes occur at `x=+-1/2(n+1/2)pi, n=0,1,2...`