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Express each one of the following in terms of trigonometric ratios of angles lying between $ 0^{\circ} $ and $ 45^{\circ} $$ \cot 85^{\circ}+\cos 75^{\circ} $
Given:
\( \cot 85^{\circ}+\cos 75^{\circ} \)
To do:
We have to express \( \cot 85^{\circ}+\cos 75^{\circ} \) in terms of trigonometric ratios of angles lying between \( 0^{\circ} \) and \( 45^{\circ} \).
Solution:
We know that,
$cot\ (90^{\circ}- \theta) = tan\ \theta$
$cos\ (90^{\circ}- \theta) = sin\ \theta$
Therefore,
$\cot 85^{\circ}+\cos 75^{\circ}=\cot (90^{\circ}-5^{\circ})+\cos (90^{\circ}-15^{\circ})$
$=\tan 5^{\circ}+\sin 15^{\circ}$
Therefore, $\cot 85^{\circ}+\cos 75^{\circ}=\tan 5^{\circ}+\sin 15^{\circ}$.
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