Evaluate the following:
$ \sin 35^{\circ} \sin 55^{\circ}-\cos 35^{\circ} \cos 55^{\circ} $

Given:

\( \sin 35^{\circ} \sin 55^{\circ}-\cos 35^{\circ} \cos 55^{\circ} \)

To do:

We have to evaluate \( \sin 35^{\circ} \sin 55^{\circ}-\cos 35^{\circ} \cos 55^{\circ} \).

Solution:  

We know that,

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

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

Therefore,

$\sin 35^{\circ} \sin 55^{\circ}-\cos 35^{\circ} \cos 55^{\circ}=\sin 35^{\circ}\sin (90^{\circ}-35^{\circ})-\cos 35^{\circ}\cos (90^{\circ}-35^{\circ})$

$=sin 35^{\circ}cos 35^{\circ}-\cos 35^{\circ}\sin 35^{\circ}$

$=0 $

Therefore, $\sin 35^{\circ} \sin 55^{\circ}-\cos 35^{\circ} \cos 55^{\circ}=0$.    

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

19 Views

Kickstart Your Career

Get certified by completing the course

Get Started