# Stationary Phase approximation of $\dfrac{1}{\pi}\int_0^{\pi}\cos(x\sin\theta-n\theta)d\theta$ (Bessel Function)

I'm trying to approximate $$\dfrac{1}{\pi}\int_0^{\pi}\cos(x\sin\theta-n\theta)d\theta$$

Where x goes to infinity I know to make it complex and then use the small angle approximation for $\sin\theta$ but I'm not sure how to proceed. Any help is greatly appreciated Thanks