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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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