NCERT Exemplar Solutions
Class 12 - Mathematics - Chapter 2: INVERSE TRIGONOMETRIC FUNCTIONS

True or False

All trigonometric functions have inverse over their respective domains.

The value of the expression \((\cos^{-1} x)^2\) is equal to \(\sec^{2} x\).

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.

The least numerical value, either positive or negative, of angle \(\theta\) is called the principal value of the inverse trigonometric function.

The graph of an inverse trigonometric function can be obtained from the graph of its corresponding trigonometric function by interchanging \(x\) and \(y\) axes.

The minimum value of \(n\) for which \(\tan^{-1} \dfrac{n}{\pi} = \dfrac{\pi}{4}\), \(n \in \mathbb{N}\), is valid is 5.

The principal value of \(\sin^{-1}\left[\cos\left(\sin^{-1} \dfrac{1}{2}\right)\right]\) is \(\dfrac{\pi}{3}\).