List of top Mathematics Questions on Properties of Inverse Trigonometric Functions asked in MET

If \(x = \sin(2\tan^{-1}2)\), \(y = \sin\left(\frac{1}{2}\tan^{-1}\frac{4}{3}\right)\), then:
If \( \alpha, \beta, \gamma \) are in AP and \( \tan^{-1}\alpha, \tan^{-1}\beta, \tan^{-1}\gamma \) are also in AP, then
If \(\tan^{-1}x + \tan^{-1}y + \tan^{-1}z = \pi\), then the value of \(x+y+z-xyz\) is
\(\sin^{-1}\frac{1}{\sqrt{5}} + \cos^{-1}\frac{3}{\sqrt{10}}\) is equal to
Evaluate: \[ \cot^{-1}\!\left(\frac{\sqrt{1+\sin x} + \sqrt{1-\sin x}}{\sqrt{1+\sin x} - \sqrt{1-\sin x}}\right) \]

If \(\sin^{-1} x + \cot^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{2}\), then value of \(x\) will be

The value of \(\tan\left[2\tan^{-1}\left(\frac{1}{5}\right) - \frac{\pi}{4}\right]\) is

The value of \(\tan\left(\frac{1}{2}\cos^{-1}\left(\frac{\sqrt{5}}{3}\right)\right)\) is
The number of solutions of the equation \(1 + \sin x \cdot \sin^2 \frac{x}{2} = 0\) in \([-\pi, \pi]\) is
The value of \(\lim_{x \to \infty} \frac{x}{x + \frac{\sqrt[3]{x}}{x + \frac{\sqrt[3]{x}}{x + \dots}}}\) is
The domain and range of \( f(x) = \sin^{-1}(x) \) are:
The number of solutions of the equation \( 2 \sin^{-1} \sqrt{x^2 - x + 1} + \cos^{-1} \sqrt{x^2 - x + 2} = \frac{3\pi}{2} \) in the interval \( [0, 5\pi] \) is
The value of \( \cos^{-1} \left( \cos \frac{7\pi}{6} \right) \) is
\( \cos^{-1}\left(\frac{-1}{2}\right) - 2\sin^{-1}\left(\frac{1}{2}\right) + 3\cos^{-1}\left(\frac{-1}{\sqrt{2}}\right) - 4\tan^{-1}(-1) \) equals
The value of \( \sin^{-1}(\sin 10) \) is:
If \( y = \tan^{-1}\left(\frac{3x - x^{3}}{1 - 3x^{2}}\right) \), then \( \frac{dy}{dx} \) is:
The value of \( \tan^{-1}(1) + \tan^{-1}(2) + \tan^{-1}(3) \) is:
The value of \( \sin^{-1}\left(\frac{2x}{1 + x^{2}}\right) \) is:
The value of \( \sin^{-1}\left(\frac{3}{5}\right) + \sin^{-1}\left(\frac{8}{17}\right) \) is:
The value of \( \sin^{-1}(\sin 10) \) is:
The value of $\sin(2 \sin^{-1} 0.8)$ is: