Evaluate:
$ \operatorname{cosec}\left(65^{\circ}+\theta\right)-\sec \left(25^{\circ}-\theta\right)-\tan \left(55^{\circ}-\theta\right)+\cot \left(35^{\circ}+\theta\right) $

Given:

\( \operatorname{cosec}\left(65^{\circ}+\theta\right)-\sec \left(25^{\circ}-\theta\right)-\tan \left(55^{\circ}-\theta\right)+\cot \left(35^{\circ}+\theta\right) \)

To do:

We have to evaluate \( \operatorname{cosec}\left(65^{\circ}+\theta\right)-\sec \left(25^{\circ}-\theta\right)-\tan \left(55^{\circ}-\theta\right)+\cot \left(35^{\circ}+\theta\right) \).

Solution:  

We know that,

$\operatorname{cosec}\ (90^{\circ}- \theta) =\sec\ \theta$

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

$\operatorname{cosec}\left(65^{\circ}+\theta\right)-\sec \left(25^{\circ}-\theta\right)-\tan \left(55^{\circ}-\theta\right)+\cot \left(35^{\circ}+\theta\right)$

$=\operatorname{cosec}(90^{\circ}-(65^{\circ}+\theta))-\sec \left(25^{\circ}-\theta\right)-\tan \left(55^{\circ}-\theta\right)+\cot (90^{\circ}-(35^{\circ}+\theta))$

$=\sec (25^{\circ}-\theta)-\sec \left(25^{\circ}-\theta\right)-\tan \left(55^{\circ}-\theta\right)+\tan (55^{\circ}-\theta)$

$=0$

Hence, $\operatorname{cosec}\left(65^{\circ}+\theta\right)-\sec \left(25^{\circ}-\theta\right)-\tan \left(55^{\circ}-\theta\right)+\cot \left(35^{\circ}+\theta\right)=0$.    

Tutorialspoint

Updated on: 10-Oct-2022

51 Views

Kickstart Your Career

Get certified by completing the course

Get Started