Question Number 71448 by aliesam last updated on 15/Oct/19
$${find}\:{the}\:{domain} \\ $$$$ \\ $$$${f}\left({x}\right)=\frac{\mathrm{1}}{{sin}\left({sin}\left({x}\right)\right)} \\ $$
Commented by kaivan.ahmadi last updated on 15/Oct/19
$${sin}\left({sinx}\right)=\mathrm{0}\Rightarrow{sinx}={k}\pi\:\:;{k}\in\mathbb{Z} \\ $$$${but}\:{since}\:−\mathrm{1}\leqslant{sinx}\leqslant\mathrm{1}\:{so}\:−\mathrm{1}\leqslant{k}\pi\leqslant\mathrm{1}\Rightarrow{k}=\mathrm{0}\Rightarrow \\ $$$${sinx}=\mathrm{0}\Rightarrow{x}={k}\pi\:\:;{k}\in\mathbb{Z} \\ $$$$\Rightarrow{D}_{{f}} =\mathbb{R}−\left\{{k}\pi\:\mid{k}\in\mathbb{Z}\right\} \\ $$