$\lim \limits_{n \to \infty}$ $\prod_{r=1}^{n} \cos(\frac{x}{2^r})$ $\lim \limits_{n \to \infty}$ $\prod_{r=1}^{n} \cos(\frac{x}{2^r})$  
How do I simplify this limit?  
I tried multiplying dividing $\sin(\frac{x}{2^r})$ to use half angle formula but it doesnt give a telescopic which would have simplified it.

$$\lim \limits_{n \to \infty} \left(\prod_{r=1}^{n} \cos\left(\frac{x}{2^r}\right)\right)=\lim \limits_{n \to \infty} \left(\frac{\sin(x)\csc\left(\frac{x}{2^n}\right)}{2^n}\right)=\frac{\sin(x)}{x}$$  
