hi

i need a little help with this domain question

let $\displaystyle f(x)=\tan (x)-\sqrt{\tan^{2}(x)-\tan (x)}$

such that $\displaystyle x \in ]\frac{-\pi}{2},\frac{+\pi}{2}[$

this is how i started :

$\displaystyle D = \left \{ x\in ]\frac{-\pi}{2},\frac{+\pi}{2}[\mid tan^{2}(x)-tan(x)\geq 0 \right \}$

next step :

$\displaystyle \forall x\in ]\frac{-\pi}{2},\frac{+\pi}{2}[$ we have $\displaystyle tan^{2}(x)-tan(x)$ $\displaystyle positive$ and so $\displaystyle tan(x) \in ]-\infty ,0]\cup [1,+\infty [$

what should i do next ?

thanks a lot