Let's see
- Denominator must not be equal to zero or the function becomes undefined
[tex]\\ \rm\rightarrowtail 1-sinx\neq 0[/tex]
[tex]\\ \rm\rightarrowtail sinx\neq 1[/tex]
[tex]\\ \rm\rightarrowtail x\neq \dfrac{n\pi}{2}[/tex]
So
[tex]\\ \rm\rightarrowtail Domain\in R-\left\{\dfrac{n\pi}{2}\right\}[/tex]
