Express $ \cos 75^{\circ}+\cot 75^{\circ} $ in terms of angles between $ 0^{\circ} $ and $ 30^{\circ} $.

Given:

\( \cos 75^{\circ}+\cot 75^{\circ} \)

To do:

We have to express \( \cos 75^{\circ}+\cot 75^{\circ} \) in terms of angles between \( 0^{\circ} \) and \( 30^{\circ} \).

Solution:  

We know that,

$cot\ (90^{\circ}- \theta) = tan\ \theta$

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

Therefore,

$\cos 75^{\circ}+\cot 75^{\circ}=\cos (90^{\circ}-15^{\circ})+\cot  (90^{\circ}-15^{\circ})$

$=\sin 15^{\circ}+\tan 15^{\circ}$

Therefore, $\cos 75^{\circ}+\cot 75^{\circ}=\sin 15^{\circ}+\tan 15^{\circ}$.   

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Updated on: 10-Oct-2022

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