Domain and range of secant and cosecant for JEE

Formula

\(\sec x\in(-\infty,-1]\cup[1,\infty),\quad \csc x\in(-\infty,-1]\cup[1,\infty)\)

Variables: \(x\in\mathbb{R}\).

Conditions: \(\sec x\) undefined when \(x=(2n+1)\pi/2\); \(\csc x\) undefined when \(x=n\pi\), \(n\in\mathbb{Z}\).

Range-based equation solving and simplification.