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, $\operatorname{cosec} 31^{\circ}-\sec 59^{\circ}=0$.   

Tutorialspoint

Updated on: 10-Oct-2022

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