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

The value of $\sin \left(\frac{1}{2}{\cos }^{-1}\frac{4}{5}\right)$ is

Mark the tick against the correct answer in the following:

${\tan }^{-1}\left\{2\cos \left(2{\sin }^{-1}\frac{1}{2}\right)\right\}=?$

Mark the tick against the correct answer in the following:

${\sin }^{-1}\left(\frac{-1}{2}\right)+2{\cos }^{-1}\left(\frac{-\sqrt{3}}{2}\right)=?$

Mark the tick against the correct answer in the following:

${\tan }^{-1}\left(-1\right)+{\cos }^{-1}\left(\frac{-1}{\sqrt{2}}\right)=?$

Mark the tick against the correct answer in the following:

${\tan }^{-1}1+{\tan }^{-1}\frac{1}{3}=?$

Mark the tick against the correct answer in the following:

${\tan }^{-1}\frac{1}{2}+{\tan }^{-1}\frac{1}{3}=?$