Domains and ranges of inverse trigonometric functions for JEE

Formula

\[\begin{aligned}\sin^{-1}x:&\ D=[-1,1],\ R=\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]\\ \cos^{-1}x:&\ D=[-1,1],\ R=[0,\pi]\\ \tan^{-1}x:&\ D=\mathbb{R},\ R=\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)\\ \cot^{-1}x:&\ D=\mathbb{R},\ R=(0,\pi)\\ \sec^{-1}x:&\ D=(-\infty,-1]\cup[1,\infty),\ R=[0,\pi]\setminus\left\{\dfrac{\pi}{2}\right\}\\ \csc^{-1}x:&\ D=(-\infty,-1]\cup[1,\infty),\ R=\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]\setminus\{0\}\end{aligned}\]

Checking validity of arguments and principal values.