Question

For what values of x, if any, does `f(x) = 1/x-tan(x)` have vertical asymptotes?

Answer 1

At `x=0` and at odd multiples of `pi/2`

Explanation:

`f(x) = 1/x-tanx = 1/x-sinx/cosx=(cosx-xsinx)/(xcosx)`

The denominator is `0` and the numerator is not at `x=0` and at odd multiples of `pi/2`.

So there are vertical asymptotes at those value of `x`.