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, $\frac{\sec 11^{\circ}}{\operatorname{cosec} 79^{\circ}}=1$.   

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

23 Views

Kickstart Your Career

Get certified by completing the course

Get Started