Hyperbola

Let $A\left(\theta_1\right)$ and $B\left(\theta_2\right)$ be two points on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and $S$ be the focus of the hyperbola, If $A, S, B$ are collinear and

a $\cos \left(\frac{\theta_1+\theta_2}{2}\right)=k \cos \left(\frac{\theta_1-\theta_2}{2}\right)$, then $k=$