The torque $\zeta$ on a body about a given point is found to be equal to $A\times L$ where $A$ is a constant vector, and $L$ is the angular momentum of the body about that point. From this it follows that

$\overrightarrow{\zeta }=\overrightarrow{A}\times \overrightarrow{L}$when $A$ is constant vector . According to given condition, it is cross product so $\overrightarrow{\zeta }$is perpendicular to $\overrightarrow{L}$and also to $\overrightarrow{A}$
The magnitude of $\overrightarrow{L}$ does not change because $\overrightarrow{\zeta }$ is perpendicular to $\overrightarrow{L}.$So $\overrightarrow{\tau } changes the direction of \overrightarrow{L} only .$

Since magnitude of $\overrightarrow{L} does not change and \overrightarrow{A} is cons\tan t , so AL\cos \theta remains cons\tan t .$