ANSWER
[tex]\tan( \alpha ) + \tan( \beta ) [/tex]
EXPLANATION
The given identity is
[tex] \frac{ \sin( \alpha + \beta ) }{ \cos( \alpha ) \cos( \beta ) } [/tex]
We expand the numerator to get:
[tex] = \frac{ \sin\alpha \cos\beta + \sin\beta \cos \alpha }{ \cos( \alpha ) \cos( \beta ) } [/tex]
Split the numerator to obtain:
[tex] = \frac{ \sin\alpha \cos\beta }{ \cos( \alpha ) \cos( \beta ) } + \frac{ \sin\beta \cos \alpha }{ \cos( \alpha ) \cos( \beta ) } [/tex]
Cancel the common factors:
[tex]= \frac{ \sin\alpha }{ \cos( \alpha ) } + \frac{ \sin\beta }{ \cos( \beta ) } [/tex]
This simplifies to give us;
[tex] = \tan( \alpha ) + \tan( \beta ) [/tex]
The second choice is correct
