Somformule:
$
\eqalign{tan \left( {\alpha + \beta } \right) = \frac{{tan \alpha + tan \beta }}
{{1 - tan \alpha \cdot tan \beta }}}
$
$
\eqalign{
& tan \left( {30^\circ + 45^\circ } \right) = \cr
& \frac{{tan 30^\circ + tan 45^\circ }}
{{1 - tan 30^\circ \cdot tan 45^\circ }} = \cr
& \frac{{\frac{1}
{3}\sqrt 3 + 1}}
{{1 - \frac{1}
{3}\sqrt 3 }} = \cr
& \frac{{\sqrt 3 + 3}}
{{3 - \sqrt 3 }} = \cr
& \frac{{6\sqrt 3 + 12}}
{6} = \cr
& \sqrt 3 + 2 \cr}
$
De afstand $x+y$ is gelijk aan:
$
\eqalign{
& \frac{9}
{{tan (60^\circ )}} + \frac{{12}}
{{tan (75^\circ )}} = \cr
& \frac{9}
{{\sqrt 3 }} + \frac{{12}}
{{2 + \sqrt 3 }} = \cr
& \frac{9}
{{\sqrt 3 }} \cdot \frac{{\sqrt 3 }}
{{\sqrt 3 }} + \frac{{12}}
{{2 + \sqrt 3 }} \cdot \frac{{2 - \sqrt 3 }}
{{2 - \sqrt 3 }} = \cr
& 3\sqrt 3 + 24 - 12\sqrt 3 = \cr
& 24 - 9\sqrt 3 \cr}
$
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