Originally Posted by

**bigwave** prove that:

$\displaystyle

\tan^{-1}{\left(\frac{1}{5}\right)}

+\tan^{-1}{\left(\frac{2}{3}\right)}

=\frac{\pi}{4}

$

first, the coordinates of $\displaystyle \frac{\pi}{4} \Rightarrow \left(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)

$

and the coordinates of

$\displaystyle

\tan^{-1}\left(\frac{1}{5}\right)

\Rightarrow \left(\frac{5}{\sqrt{26}},\frac{1}{\sqrt{26}}\righ t)

$

and

$\displaystyle

\tan^{-1}\left(\frac{2}{3}\right)

\Rightarrow \left(\frac{3}{\sqrt{13}},\frac{2}{\sqrt{13}}\righ t)

$

so thot from these that using $\displaystyle \cos{\left(\alpha + \beta\right)}$ I could get the coordinates of $\displaystyle \frac{\pi}{4}$

but did not unless I made an error somewhere....