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, $\cot 85^{\circ}+\cos 75^{\circ}=\tan 5^{\circ}+\sin 15^{\circ}$.   

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

39 Views

Kickstart Your Career

Get certified by completing the course

Get Started