Evaluate each of the following:

(i) `"c o s e c"^(-1)("c o s e c"(6pi)/5)`

(ii) `"c o s e c"^(-1)("c o s e c"(11pi)/6)`

Explanation

(i)
We know that
$$
\begin{aligned}
&\operatorname{cosec}^{-1}(\operatorname{cosec} \theta)=\theta, \quad[-\pi / 2,0) \cup(0, \pi / 2] \\
&\operatorname{cosec}^{-1}\left(\operatorname{cosec} \frac{6 \pi}{5}\right)=\operatorname{cosec}^{-1}\left[\operatorname{cosec}\left(\pi+\frac{\pi}{5}\right)\right] \\
&=\operatorname{cosec}^{-1}\left(\operatorname{cosec}-\frac{\pi}{5}\right) \\
&=-\frac{\pi}{5}
...