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Evaluate the following:
$ \operatorname{cosec} 31^{\circ}-\sec 59^{\circ} $
Given:
\( \operatorname{cosec} 31^{\circ}-\sec 59^{\circ} \)
To do:
We have to evaluate \( \operatorname{cosec} 31^{\circ}-\sec 59^{\circ} \).
Solution:
We know that,
$sec (90^{\circ}- \theta) = cosec\ \theta$
Therefore,
$\operatorname{cosec} 31^{\circ}-\sec 59^{\circ}=\operatorname{cosec} 31^{\circ}-\sec (90^{\circ}-31^{\circ})$
$=\operatorname{cosec} 31^{\circ}-\operatorname{cosec} 31^{\circ}$
$=0$
Therefore, $\operatorname{cosec} 31^{\circ}-\sec 59^{\circ}=0$.
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