Question:
What is the maximum value of $\frac{1}{\operatorname{cosec} \theta} ?$
Solution:
The maximum value of $\frac{1}{\operatorname{cosec} \theta}$ is 1 because the maximum value of $\sin \theta$ is 1 that is
$\frac{1}{\operatorname{cosec} \theta}=\sin \theta$
$\frac{1}{\operatorname{cosec} \theta}=1$