$e^{\log (\cosh^{-1} 2)}$ is equal to :

If $\operatorname{Tanh}^{-1} x = \operatorname{Coth}^{-1} y = \log \sqrt{5}$,then $\operatorname{Tan}^{-1}(xy) = $

The value of $\tan^{-1} \left( \frac{\cos(\frac{19\pi}{4}) - 1}{\sin(\frac{\pi}{4})} \right)$ is equal to

If the area of the region bounded by the parabola $y^2 = 4kx$ and the line $x = k$ (where $k > 0$) is $\frac{128}{3} \text{ sq. units}$, then the value of $\sin^{-1}(\frac{2}{k})$ is equal to...

The value of $\sin ^{-1}\left(\frac{-1}{2}\right)+\sin ^{-1}\left(\frac{-\sqrt{3}}{2}\right)$ is

If $x = \tan^{-1} \left(\frac{1}{5}\right) + \tan^{-1} \left(\frac{1}{8}\right)$, then $\frac{\sin x + \cos x}{\tan x} = $