List of top Mathematics Questions on Inverse Trigonometric Functions asked in COMEDK UGET

Evaluate: $ \cot^{-1} \left( -\frac{3}{\sqrt{3}} \right) - \sec^{-1} \left( -\frac{2}{\sqrt{2}} \right) - \csc^{-1}(-1) - \tan^{-1}(1) $
The value of \[ \sin^{-1} \left[ \cos \left( \frac{39\pi}{5} \right) \right] \] is
Let \[ f(x) = \cos^{-1}(3x - 1) \] then the domain of \( f(x) \) is equal to}
$\cot^{-1} (21) + \cot^{-1} (13) + \cot^{-1} (-8) =$
If $\tan(x + y) = 33$ and $x = \tan^{-1} \, 3,$ then $y$ is
$\tan\left(\cos^{-1}\left( \frac{1}{5\sqrt{2}}\right)-\sin^{-1}\left(\frac{4}{\sqrt{17}}\right)\right)$ is
$\int \frac{e^{x} \left(1 +\sin x\right)}{1+\cos x}dx= $
If $\cos^{-1} x +\cos^{-1} y +\cos^{-1}z = 3\pi $, then $xy + yz + zx$ is
$\tan^{-1} \left(\frac{1}{x+y} \right) +\tan ^{-1}\left(\frac{y}{x^{2} +xy +1}\right)= $
If $\frac{1}{2} \leq x \leq 1, $ then $\cos^{-1} x +\cos ^{-1}\left(\frac{x}{2} +\frac{\sqrt{3-3x^{2}}}{2}\right) =$
The value of $\tan^{-1} \frac{\sqrt{2+\sqrt{3}} -\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3} } +\sqrt{2-\sqrt{3}}} $
$\tan\left[\frac{1}{2} \sin^{-1} \left(\frac{2x}{1+x^{2}}\right) + \frac{1}{2} \cos^{-1} \left(\frac{1-x^{2}}{1+x^{2}}\right)\right] = $
Define $f (x) = min{x^2 + 1, x + 1]$ for.$x e\in R$. Then $ \int\limits_{-1}^1f (x)dx $ is
The value of the integral $\int\limits_{0}^{\pi/ 4} \frac{1+\sin^{2} }{ \cos^{3} x} dx $ is