Answer:
[tex]\mathbb{R}-(n\pi+\frac{\pi}{2})[/tex]
Step-by-step explanation:
We have, [tex]\text{y}=\text{sec} x[/tex]
This can also be written as [tex]\text{y}=\frac{1}{\text{cos} x}[/tex]
For this to be defined, [tex]\text{cos}x\neq 0[/tex]
So, the function is defined for all real numbers except when [tex]\text{cos}x=0[/tex]
i.e., for [tex]x=(2n+1)\frac{\pi }{2}\text{or}x=n\pi+\frac{\pi}{2}[/tex]
Therefore, the domain of [tex]\text{y}=\text{sec} x[/tex] is [tex]\mathbb{R}-(n\pi+\frac{\pi}{2})[/tex]
