Evaluate : $$\cos ^{-1}\left[\cos \left(-680^{\circ}\right)\right]+\sin ^{-1}\left[\sin \left(-600^{\circ}\right)\right]-\cos ^{-1}\left(\sin 270^{\circ}\right)$$

$$ \text { The value of } \sin ^{-1}\left[\cot \left(\frac{1}{2} \tan ^{-1} \frac{1}{\sqrt{3}}+\cos ^{-1} \frac{\sqrt{12}}{4}+\sin ^{-1} \frac{1}{\sqrt{2}}\right)\right] $$ is

$$ \text { Let } f(x)=\cos ^{-1}(3 x-1) \text {, then domain of } f(x) \text { is equal to } $$

$$ \text { The value of } \sin ^{-1}\left[\cos \left(39 \frac{\pi}{5}\right)\right] \text { is } $$