Express each one of the following in terms of trigonometric ratios of angles lying between $ 0^{\circ} $ and $ 45^{\circ} $$ \sec 76^{\circ}+\operatorname{cosec} 52^{\circ} $

Given:

\( \sec 76^{\circ}+\operatorname{cosec} 52^{\circ} \)

To do:

We have to express \( \sec 76^{\circ}+\operatorname{cosec} 52^{\circ} \) in terms of trigonometric ratios of angles lying between \( 0^{\circ} \) and \( 45^{\circ} \).

Solution:  

We know that,

$sec\ (90^{\circ}- \theta) = cosec\ \theta$

$\operatorname{cosec}\ (90^{\circ}- \theta) = sec\ \theta$

Therefore,

$\sec 76^{\circ}+\operatorname{cosec} 52^{\circ}=\sec (90^{\circ}-14^{\circ})+\operatorname{cosec} (90^{\circ}-38^{\circ})$

$=\operatorname{cosec} 14^{\circ}+\sec 38^{\circ}$

Therefore, $\sec 76^{\circ}+\operatorname{cosec} 52^{\circ}=\operatorname{cosec} 14^{\circ}+\sec 38^{\circ}$.   

Tutorialspoint

Updated on: 10-Oct-2022

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