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

Fill in the Blanks

The principal value of \(\cos^{-1}(-\dfrac{1}{2})\) is ____.

The value of \(\sin^{-1}\left(\sin \dfrac{3\pi}{5}\right)\) is ____.

If \(\cos(\tan^{-1} x + \cot^{-1} \sqrt{3}) = 0\), then value of \(x\) is ____.

The set of values of \(\sec^{-1}\left(\dfrac{1}{2}\right)\) is ____.

The principal value of \(\tan^{-1} \sqrt{3}\) is ____.

The value of \(\cos^{-1}(\cos \dfrac{14\pi}{3})\) is ____.

The value of \(\cos(\sin^{-1} x + \cos^{-1} x)\), \(|x| \le 1\), is ____.

The value of the expression \(\tan\left(\dfrac{\sin^{-1} x + \cos^{-1} x}{2}\right)\), when \(x = \dfrac{\sqrt{3}}{2}\), is ____.

If \(y = 2 \tan^{-1} x + \sin^{-1}\left(\dfrac{2x}{1 + x^{2}}\right)\) for all \(x\), then ____ < y < ____.

The result \(\tan^{-1} x - \tan^{-1} y = \tan^{-1}\left(\dfrac{x - y}{1 + xy}\right)\) is true when value of \(xy\) is ____.

The value of \(\cot^{-1}(-x)\) for all \(x \in \mathbb{R}\) in terms of \(\cot^{-1} x\) is ____.