List of top Mathematics Questions on Inverse Trigonometric Functions asked in CBSE CLASS XII

Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

Evaluate : $\tan^{-1}\left(-\frac{1}{\sqrt{3}}\right) + \cot^{-1}\left(\frac{1}{\sqrt{3}}\right) + \tan^{-1}\left(\sin\left(-\frac{\pi}{2}\right)\right) + \tan^{-1}\left(\tan\left(\frac{2\pi}{3}\right)\right)$}

The graph of an inverse trigonometric function passes through the point $(0, \frac{\pi}{2})$ with asymptotes at $y = 0$ and $y = \pi$. This graph represents the function:

Find the value of \( \sin [\cot^{-1} \sqrt{2} (\cos (\tan^{-1} 1))] \).

The principal value of \( \cot^{-1} \left( -\frac{1}{\sqrt{3}} \right) \) is:

Assertion (A): The set of values of $\sec^{-1} \left( \frac{\sqrt{3}}{2} \right)$ is a null set.
Reason (R): $\sec^{-1}x$ is defined for $x \in \mathbb{R} - (-1, 1)$.

The principal value of \( \cot^{-1} \left( -\frac{1}{\sqrt{3}} \right) \) is: