.toggle().attr() true/false study

HTML

<input type="button" value="Toggle" aria-controls="myDiv" />
<div id="myDiv" aria-expanded="false">Hello world.</div>

JavaScript

$('input[type="button"]').click(function () {
    var $tar = $('#' + $(this).attr('aria-controls'));
        $tar.toggle().attr('aria-expanded', !$tar.attr('aria-expanded'));
});