Find the angle ?

**Kluringen** · September 12th 2009, 02:42 PM

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 $tan(x)$ ?

**skeeter** · September 12th 2009, 03:37 PM

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 $tan(x)$ ?

$\tan{x} = \tan(\arctan{7} + 2\arctan{3})<br />$

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

intermediate step ...

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

evaluate ...

$\tan{x} = \frac{7 -\frac{3}{4}}{1 + \frac{21}{4}} = 1<br />$

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