Express each one of the following in terms of trigonometric ratios of angles lying between $ 0^{\circ} $ and $ 45^{\circ} $$ \cos 78^{\circ}+\sec 78^{\circ} $

Given:

\( \cos 78^{\circ}+\sec 78^{\circ} \)

To do:

We have to express \( \cos 78^{\circ}+\sec 78^{\circ} \) in terms of trigonometric ratios of angles lying between \( 0^{\circ} \) and \( 45^{\circ} \).

Solution:  

We know that,

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

$cos (90^{\circ}- \theta) = sin\ \theta$

Therefore,

$\cos 78^{\circ}+\sec 78^{\circ}=\cos (90^{\circ}-12^{\circ})+\sec (90^{\circ}-12^{\circ})$

$=\sin 12^{\circ}+cosec 12^{\circ}$

Therefore, $\cos 78^{\circ}+\sec 78^{\circ}=\sin 12^{\circ}+cosec 12^{\circ}$.   

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Updated on: 10-Oct-2022

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