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