# Math Help - Find the angle ?

1. ## Find the angle ?

Hi!
In this problem I need to find the exact value of $tan(x)$ and the $x=arctan7+2arctan 3$. How can I find the angle for $tan(x)$?

2. Originally Posted by Kluringen
Hi!
In this problem I need to find the exact value of $tan(x)$ and the $x=arctan7+2arctan 3$. How can I find the angle for $tan(x)$?
$\tan{x} = \tan(\arctan{7} + 2\arctan{3})
$

$\tan{x} = \frac{\tan(\arctan{7}) + \tan(2\arctan{3})}{1 - \tan(\arctan{7})\tan(2\arctan{3})}
$

intermediate step ...

$\tan(2\arctan{3}) = \frac{2\tan(\arctan{3})}{1 - \tan^2(\arctan{3})} = -\frac{3}{4}
$

evaluate ...

$\tan{x} = \frac{7 -\frac{3}{4}}{1 + \frac{21}{4}} = 1
$