If in a $\triangle ABC$, $CD$ is the angle bisector of the angle $ACB$, then $CD=\displaystyle \frac { kab }{ a+b } \cos { \frac { C }{ 2 } } $

By the angle bisector length formula, the length of the bisector from vertex $C$ is given by $CD = \frac{2ab \cos(C/2)}{a + b}$. This formula is derived by equating the areas of triangles $ACD$ and $BCD$ to half the area of triangle $ABC$. Comparing this standard formula with the provided expression $\frac{kab}{a+b} \cos(C/2)$, we find that $k$ equals $2$.

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