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

Objective Type Question

Which of the following is the principal value branch of \(\cos^{-1} x\)?

Which of the following is the principal value branch of \(\csc^{-1} x\)?

If \(3 \tan^{-1} x + \cot^{-1} x = \pi\), then \(x\) equals

The value of \(\sin^{-1}\left(\cos \dfrac{33\pi}{5}\right)\) is

The domain of the function \(\cos^{-1}(2x - 1)\) is

The domain of the function defined by \(f(x) = \sin^{-1} \sqrt{x - 1}\) is

If \(\cos\left(\sin^{-1} \dfrac{2}{5} + \cos^{-1} x\right) = 0\), then \(x\) is equal to

The value of \(\sin(2 \tan^{-1}(0.75))\) is equal to

The value of \(\cos^{-1}(\cos \dfrac{3\pi}{2})\) is equal to

The value of the expression \(2 \sec^{-1} 2 + \sin^{-1} \left(\dfrac{1}{2}\right)\) is

If \(\tan^{-1} x + \tan^{-1} y = \dfrac{4\pi}{5}\), then \(\cot^{-1} x + \cot^{-1} y\) equals

If \(\sin^{-1}\left(\dfrac{2a}{1 + a^{2}}\right) + \cos^{-1}\left(\dfrac{1 - a^{2}}{1 + a^{2}}\right) = \tan^{-1}\left(\dfrac{2x}{1 - x^{2}}\right)\), where \(a, x \in (0, 1)\), then the value of \(x\) is

The value of \(\cot \left[ \cos^{-1} \left(\dfrac{7}{25}\right) \right]\) is

The value of the expression \(\tan\left(\dfrac{1}{2} \cos^{-1} \dfrac{2}{\sqrt{5}}\right)\) is

If \(x \le 1\), then \(2 \tan^{-1} x + \sin^{-1}\left(\dfrac{2x}{1 + x^{2}}\right)\) is equal to

If \(\cos^{-1} \alpha + \cos^{-1} \beta + \cos^{-1} \gamma = 3\pi\), then \(\alpha(\beta + \gamma) + \beta(\gamma + \alpha) + \gamma(\alpha + \beta)\) equals

The number of real solutions of the equation \(\sqrt{1 + \cos 2x} = \sqrt{2} \cos^{-1}(\cos x)\) in \([\dfrac{\pi}{2}, \pi]\) is

If \(\cos^{-1} x > \sin^{-1} x\), then