a.
Met de cosinuregel:
$
\begin{array}{l}
\left. \begin{array}{l}
4^2 = 5^2 + 6^2 - 2 \times 5 \times 6 \times \cos \alpha \Rightarrow \cos \alpha = \frac{3}{4}\,\,en\,\,\sin \alpha = \frac{1}{4}\sqrt 7 \\
6^2 = 4^2 + 5^2 - 2 \times 4 \times 5 \times \cos \gamma \Rightarrow \cos \gamma = \frac{1}{8}\,\,en\,\,\sin \gamma = \frac{3}{8}\sqrt 7 \\
\end{array} \right\} \Rightarrow \\
\sin (2\alpha ) = 2\,\sin \alpha \cos \alpha = 2\, \times \frac{1}{4}\sqrt 7 \times \frac{3}{4} = \frac{3}{8}\sqrt 7 = \sin \gamma \Rightarrow \gamma = 2\alpha \\
\end{array}
$
b.
$
\eqalign{\tan \left( {\frac{1}{2}\alpha } \right) = \frac{{\sin \alpha }}{{1 + \cos \alpha }} = \frac{{\frac{1}{4}\sqrt 7 }}{{1 + \frac{3}{4}}} = \frac{1}{7}\sqrt 7}
$
Zie eventueel Wikipedia | Lijst van goniometrische gelijkheden
WvR
9-1-2010