csc^-1(2)= 30 degrees or 0.523598775598.
cot^-1(-sqrt3)= -30 degrees or -0.523598775598.
$$csc^{-1}(2)\\\\
=sin^{-1}\left(\frac{1}{2}\right)\\\\
= 30^0 \quad or \quad \frac{\pi}{6}\;radians\\\\\\
cot^{-1}(-\sqrt3)\\\\
=tan^{-1}\left(\frac{-1}{\sqrt3}\right)\\\\
=tan^{-1}\left(\frac{-1}{\sqrt3}\right)\\\\
= -30^0 \quad or \quad \frac{-\pi}{6}\;radians\\\\\\$$