i need to prove that the function $\displaystyle f(x)= 2tanx-\frac{1}{cosx}$ gets every real value in the open range $\displaystyle (-\frac{\pi}{2},\frac{\pi}{2}) $

what i was able to do so far is to translate the function to: $\displaystyle \frac{2sinx-1}{cosx}$ and say..

let t>0 (at R); i know that $\displaystyle f(0)=-1 $, so what is left for me to do in order to use Intermidate Value Theorem is to find a point which is bigger than t. but i'm stuck...