The domain of y = csc x is given by x≠nπ. True or False?

Answer:True          Step-by-step explanation: Given : The domain of [tex]y = csc x[/tex] is given by [tex]x\neq n\pi[/tex]The given statement is true. Because,  [tex]y = csc x[/tex] [tex]y =\frac{1}{sinx}{[/tex][tex]sinx[/tex] is defined for [tex]\forall x\varepsilon \mathbb{R}[/tex] [tex] csc x[/tex]is defined whenever [tex]sinx\neq 0\rightarrow x\neq n\pi,\forall n\varepsilon \mathbb{Z}[/tex] Hence the domain of y is all[tex]x\varepsilon \mathbb{R}: x\neq 0\rightarrow x\neq n\pi,\forall n\varepsilon \mathbb{Z}[/tex]Therefore, the statement is true as the domain of [tex]y = csc x[/tex] is [tex]x\varepsilon \mathbb{R}: x\neq 0\rightarrow x\neq n\pi,\forall n\varepsilon \mathbb{Z}[/tex]