OMG ... It's all about a pair of parentheses () !!
Even I was surprised at first sight, how can that code give some errors ?!

Finally found it, though. Here is the rectified code :

Code: JavaScript
function check()
{
    var a=document.getElementById("txt_user").value.trim();
    var b=document.getElementById("txt_pwd").value.trim();
    if((a=="")||(b==""))
    {
        alert("Required fields can't be left empty");
        return false;
    }
    else if(a==b)
    {
        alert("Username and password are same");
        return false;
    }
}

You missed a pair of parentheses behind the trim function.