Infintite product true or not

It doesn't seem right to me, try x = 2pi.

 

Try x = pi.

 

No, your infintite product does not even converge.

Infinite product form for sine:

[tex]\sin(x)=x\prod_{n=1}^{\infty}\left(1-\frac{x^2}{(\pi n)^2} \right)[/tex]

 

I was trying to point out that sin(pi) = 0 but your serie would never go to 0.

 

Still doesn't converge, the absolute value of the terms is growing without bound.