According to the sad situation in nowadays front-end development, we have to check current browser type and version in JavaScript code and behave differently depend on that. There are many options to do so like this or this. But working in SharePoint 2010 environment you have one more, init.js defines browseris object (see on the picture below) which contains most of required data. Be free to rely on SharePoint in this case.
How to determine browser type in JavaScript (for SharePoint 2010 sites)
Sergey Tihon's Blog 