Hi!
In this problem I need to find the exact value of $\displaystyle tan(x)$ and the $\displaystyle x=arctan7+2arctan 3$. How can I find the angle for $\displaystyle tan(x)$?
$\displaystyle \tan{x} = \tan(\arctan{7} + 2\arctan{3})
$
$\displaystyle \tan{x} = \frac{\tan(\arctan{7}) + \tan(2\arctan{3})}{1 - \tan(\arctan{7})\tan(2\arctan{3})}
$
intermediate step ...
$\displaystyle \tan(2\arctan{3}) = \frac{2\tan(\arctan{3})}{1 - \tan^2(\arctan{3})} = -\frac{3}{4}
$
evaluate ...
$\displaystyle \tan{x} = \frac{7 -\frac{3}{4}}{1 + \frac{21}{4}} = 1
$