$\cot \left[ \cos^{-1} \left( \frac{7}{25} \right) \right] = $

$\sin (2{\sin ^{ - 1}}0.8) = $

$\sin ^{-1}\left(\sin \frac{23 \pi}{6}\right) = $ . . . . . . .

The value of $\tan ^{-1}\left(\frac{\cos \left(\frac{15 \pi}{4}\right)-1}{\sin \left(\frac{\pi}{4}\right)}\right)$ is equal to

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

The value of $\sin \left(2 \sin ^{-1} 0.8\right)$ is equal to