Question

Help!!!! Question is attached in photo

Answer 1

ANSWER

$\tan( \alpha ) + \tan( \beta )$

EXPLANATION

The given identity is

$\frac{ \sin( \alpha + \beta ) }{ \cos( \alpha ) \cos( \beta ) }$

We expand the numerator to get:

$= \frac{ \sin\alpha \cos\beta + \sin\beta \cos \alpha }{ \cos( \alpha ) \cos( \beta ) }$

Split the numerator to obtain:

$= \frac{ \sin\alpha \cos\beta }{ \cos( \alpha ) \cos( \beta ) } + \frac{ \sin\beta \cos \alpha }{ \cos( \alpha ) \cos( \beta ) }$

Cancel the common factors:

$= \frac{ \sin\alpha }{ \cos( \alpha ) } + \frac{ \sin\beta }{ \cos( \beta ) }$

This simplifies to give us;

$= \tan( \alpha ) + \tan( \beta )$

The second choice is correct