Answer:
tana + tanb
Step-by-step explanation:
Using the trigonometric identities
• sin(a + b) = sinacosb + cosasinb
• tanx = [tex]\frac{sinx}{cosx}[/tex], then
[tex]\frac{sin(a+b)}{cosacosb}[/tex]
= [tex]\frac{sinacosb+cosasinb}{cosacosb}[/tex]
= [tex]\frac{sinacosb}{cosacosb}[/tex] + [tex]\frac{cosasinb}{cosacosb}[/tex]
= [tex]\frac{sina}{cosa}[/tex] + [tex]\frac{sinb}{cosb}[/tex]
= tana + tanb
