If $A = \tan^{-1}x$,then $\sin 2A = $

The value of $\sin^{-1}\left(\sin \frac{7 \pi}{6}\right)$ is equal to . . . . . . .

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

If $\sin ^{-1} x=y,$ then

If $y = \cos^{-1}(\cos(|x| - f(x)))$,where $f(x) = \begin{cases} 1, & \text{if } x > 0 \\ -1, & \text{if } x < 0 \\ 0, & \text{if } x = 0 \end{cases}$,then $\left. \frac{dy}{dx} \right|_{x = \frac{5\pi}{4}}$ is

Write the function in the simplest form: $\tan ^{-1}\left(\sqrt{\frac{1-\cos x}{1+\cos x}}\right), x < \pi$