Optimisation to solve for trigonometric expression? 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!

Since $\left|-\dfrac{\sqrt{3}}{2}\right|\le 1$, we have that $\cos^{-1}\left( -\dfrac{\sqrt{3}}{2}\right)+\sin^{-1}\left( -\dfrac{\sqrt{3}}{2}\right) =\dfrac{\pi}{2} $.
So $\operatorname{cosec} \left( \cos^{-1}\left( -\dfrac{\sqrt{3}}{2}\right)+\sin^{-1}\left( -\dfrac{\sqrt{3}}{2}\right)\right)=\operatorname{cosec} \left(\dfrac{\pi}{2}\right) =\dfrac{1}{\sin \left(\dfrac{\pi}{2}\right)}=1 $.
