All trigonometric functions have inverse over their respective domains.
False
The value of the expression \((\cos^{-1} x)^2\) is equal to \(\sec^{2} x\).
False
The domain of trigonometric functions can be restricted to any one of their branches (not necessarily principal value) in order to obtain their inverse functions.
True
The least numerical value, either positive or negative, of angle \(\theta\) is called the principal value of the inverse trigonometric function.
True
The graph of an inverse trigonometric function can be obtained from the graph of its corresponding trigonometric function by interchanging \(x\) and \(y\) axes.
True
The minimum value of \(n\) for which \(\tan^{-1} \dfrac{n}{\pi} = \dfrac{\pi}{4}\), \(n \in \mathbb{N}\), is valid is 5.
False
The principal value of \(\sin^{-1}\left[\cos\left(\sin^{-1} \dfrac{1}{2}\right)\right]\) is \(\dfrac{\pi}{3}\).
True