Question

verify cos(a+b)/cos(a) cos(b) =1-tan(a) tan(b)

Answer 1

The identity as been verified/proved as:

$1 - \tan\ a\ tan\ b = 1 - \tan\ a\ tan\ b$

Given that:

$\frac{\cos(a + b)}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b$

Apply cosine identity to the numerator

$\frac{\cos\ a\ cos\ b - \sin a\ sin\ b}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b$

Split the fraction:

$\frac{\cos\ a\ cos\ b}{\cos\ a\cos b} - \frac{\sin a\ sin\ b}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b$

Cancel out common terms

$1 - \frac{\sin a\ sin\ b}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b$

In trigonometry, we have:

$\frac{\sin \theta}{\cos \theta} = \tan \theta$

So, the equation becomes:

$1 - \tan\ a\ tan\ b = 1 - \tan\ a\ tan\ b$

Hence, the identity has been verified

Read more about trigonometry identities at:

https://brainly.com/question/21055284