JSFiddle - React, Tailwind, and code Playground
HTML
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css">
<script src="https://code.jquery.com/jquery-3.2.1.min.js"></script>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js"></script>
<nav class="navbar navbar-inverse navbar-static-top">
<div class="container-fluid">
<ul class="nav navbar-nav">
<li class="dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#">Page 1 <span class="glyphicon glyphicon-chevron-down"></span></a>
<ul class="dropdown-menu">
<li><a href="#">Page 1-1</a></li>
<li><a href="#">Page 1-2</a></li>
<li><a href="#">Page 1-3</a></li>
</ul>
</li>
<li class="dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#">Page 2 <span class="glyphicon glyphicon-chevron-down"></span></a>
<ul class="dropdown-menu">
<li><a href="#">Page 1-1</a></li>
<li><a href="#">Page 1-2</a></li>
<li><a href="#">Page 1-3</a></li>
</ul>
</li>
<li class="dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#">Page 3 <span class="glyphicon glyphicon-chevron-down"></span></a>
<ul class="dropdown-menu">
<li><a href="#">Page 1-1</a></li>
<li><a href="#">Page 1-2</a></li>
<li><a href="#">Page 1-3</a></li>
</ul>
</li>
</ul>
</div>
</nav>
JavaScript
$(function() {
// THIS WILL FIRE WHENEVER DROPDOWN SHOW
$('.nav > li.dropdown').on('show.bs.dropdown', function () {
$(this).find('.glyphicon').removeClass('glyphicon-chevron-down').addClass('glyphicon-chevron-up');
});
// THIS WILL FIRE WHENEVER DROPDOWN HIDE
$('.nav > li.dropdown').on('hide.bs.dropdown', function () {
$(this).find('.glyphicon').removeClass('glyphicon-chevron-up').addClass('glyphicon-chevron-down');
});
});