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]
