I have a question that requires the use of optimisation to solve for the following expression:

$$\cos ec{(\cos^{-1}{(-\frac{\sqrt{3}}{2})}+\sin^{-1}{(-\frac{\sqrt{3}}{2})})}$$

I'm a bit baffled, as I'm not sure whether this refers to finding the value of cosec or finding the value of cos(ec)(cos^(-1)...). No further clarity is given.

Without using optimisation, the expression can just be evaluated at face-value to:

$$\csc{(\frac{5\pi}{6}+\frac{4\pi}{3})} = \csc{(2\pi+\frac{\pi}{6})} = \frac{1}{\sin{\frac{\pi}{6}}} = \frac{1}{\frac{1}{2}} = 2$$

Any suggestions would be appreciated!