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Evaluate the following:$ \frac{\sec 11^{\circ}}{\operatorname{cosec} 79^{\circ}} $
Given:
\( \frac{\sec 11^{\circ}}{\operatorname{cosec} 79^{\circ}} \)
To do:
We have to evaluate \( \frac{\sec 11^{\circ}}{\operatorname{cosec} 79^{\circ}} \).
Solution:
We know that,
$\operatorname{cosec}\ (90^{\circ}- \theta) = sec\ \theta$
Therefore,
$\frac{\sec 11^{\circ}}{\operatorname{cosec} 79^{\circ}}=\frac{\sec 11^{\circ}}{\operatorname{cosec} (90^{\circ}-11^{\circ})}$
$=\frac{\sec 11^{\circ}}{\sec 11^{\circ}}$
$=1$
Therefore, $\frac{\sec 11^{\circ}}{\operatorname{cosec} 79^{\circ}}=1$.
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