Given that $\displaystyle \frac{cos(A-B)}{cos(A+B)}=\frac{7}{5}$, prove that $\displaystyle cosAcosB = 6sinAsinB$ and deduce a relationship between $\displaystyle tanA$ and $\displaystyle tanB$. Given further that $\displaystyle A+B=45^\circ$, calculate the value of $\displaystyle tanA+tanB$.

I have already proved the equation.

I have also tried to deduce the relationship between tanA and tanB,

$\displaystyle cosAcosB=6sinAsinB$

$\displaystyle \frac{cosAcosB}{sinAsinB}=\frac{1}{6}$

[Math]tanAtanB=\frac{1}{6}[/tex]

But am not sure if I am on the right track. Lastly, need help with calculating the value of $\displaystyle tanA+tanB$