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

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

$\sin^{-1} (\sin \frac{3\pi}{5}) = \dots \dots \dots$

Consider the following statements:
Statement-$I$: $\operatorname{Cosh}^{-1} x = \operatorname{Tanh}^{-1} x$ has no solution.
Statement-$II$: $\operatorname{Cosh}^{-1} x = \operatorname{Coth}^{-1} x$ has only one solution.
The correct answer is:

The value of $\cos ^{-1}\left(\cos \left(\frac{7 \pi}{6}\right)\right)$ is

$A$ value of $x$ for which $\sin(\cot^{-1}(1 + x)) = \cos(\tan^{-1}x)$ is