Express each one of the following in terms of trigonometric ratios of angles lying between $ 0^{\circ} $ and $ 45^{\circ} $$ \tan 65^{\circ}+\cot 49^{\circ} $

Given:

\( \tan 65^{\circ}+\cot 49^{\circ} \)

To do:

We have to express \( \tan 65^{\circ}+\cot 49^{\circ} \) in terms of trigonometric ratios of angles lying between \( 0^{\circ} \) and \( 45^{\circ} \).

Solution:  

We know that,

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

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

Therefore,

$\tan 65^{\circ}+\cot 49^{\circ}=\tan (90^{\circ}-25^{\circ})+\cot  (90^{\circ}-41^{\circ})$

$=\cot 25^{\circ}+\tan 41^{\circ}$

Therefore, $\tan 65^{\circ}+\cot 49^{\circ}=\cot 25^{\circ}+\tan 41^{\circ}$.   

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Updated on: 10-Oct-2022

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