changing dynamic web page lanuguage

Sadly, for that you will need to reload the HTML content. Or at least you will need to update the elements to render a different content view.

But my suggestion would be, to reload the page when the dropdownlist changes its value. For example, such as this:

You will then now add this function as the handler for the value change. This would redirect the user to the page, where he would read the content in their desired language.

Then at the backend, you will use ASP.NET's localization to render different content based on the language they are interested in. Read the MSDN article that I have attached below. This way, you can do the thing that you want to do.

https://msdn.microsoft.com/en-us/library/c6zyy3s9.aspx