Like Eliran Malka asked, why do you need to check for IE 9?

Detecting browser make and version is generally a bad smell. This generally means that you there is a bigger problem with the code if you need JavaScript to detect specific versions of browser.

There are genuine cases where a feature won't work, like say WebSockets isn't supported in IE 8 or 9. This should be solved by checking for WebSocket support, and applying a polyfill if there is no native support.

This should be done with a library like Modernizr.

That being said, you can easily create service that would return the browser. There are valid cases where a feature exists in a browser but the implementation is outdated or broken. Modernizr is not appropriate for these cases.

app.service('browser', ['$window', function($window) {

     return function() {

         var userAgent = $window.navigator.userAgent;

        var browsers = {chrome: /chrome/i, safari: /safari/i, firefox: /firefox/i, ie: /internet explorer/i};

        for(var key in browsers) {
            if (browsers[key].test(userAgent)) {
                return key;
            }
       };

       return 'unknown';
    }

}]);

Fixed typo broswers

Note: This is just an example of how to create a service in angular that will sniff the userAgent string. This is just a code example that is not expected to work in production and report all browsers in all situations.

UPDATE

It is probably best to use a third party library like https://github.com/ded/bowser or https://github.com/darcyclarke/Detect.js. These libs place an object on the window named bowser or detect respectively.

You can then expose this to the Angular IoC Container like this:

angular.module('yourModule').value('bowser', bowser);

Or

detectFactory.$inject = ['$window'];
function detectFactory($window) {
    return detect.parse($window.navigator.userAgent);
} 
angular.module('yourModule').factory('detect', detectFactory);

You would then inject one of these the usual way, and use the API provided by the lib. If you choose to use another lib that instead uses a constructor method, you would create a factory that instantiates it:

function someLibFactory() {
    return new SomeLib();
}
angular.module('yourModule').factory('someLib', someLibFactory);

You would then inject this into your controllers and services the normal way.

If the library you are injecting does not exactly match your requirements, you may want to employ the Adapter Pattern where you create a class/constructor with the exact methods you need.

In this example we just need to test for IE 9, and we are going to use the bowser lib above.

BrowserAdapter.$inject = ['bowser']; // bring in lib
function BrowserAdapter(bowser) {
    this.bowser = bowser;
}

BrowserAdapter.prototype.isIe9 = function() {
    return this.bowser.msie && this.browser.version == 9;
}

angular.module('yourModule').service('browserAdapter', BrowserAdapter);

Now in a controller or service you can inject the browserAdapter and just do if (browserAdapter.isIe9) { // do something }

If later you wanted to use detect instead of bowser, the changes in your code would be isolated to the BrowserAdapter.

UPDATE

In reality these values never change. IF you load the page in IE 9 it will never become Chrome 44. So instead of registering the BrowserAdapter as a service, just put the result in a value or constant.

angular.module('app').value('isIe9', broswerAdapter.isIe9);

Angular library uses document.documentMode to identify IE . It holds major version number for IE, or NaN/undefined if User Agent is not IE.

/**
* documentMode is an IE-only property
* http://msdn.microsoft.com/en-us/library/ie/cc196988(v=vs.85).aspx
*/
var msie = document.documentMode;

https://github.com/angular/angular.js/blob/v1.5.0/src/Angular.js#L167-L171

Example with $document (angular wrapper for window.document)

// var msie = document.documentMode;
var msie = $document[0].documentMode;
// if is IE (documentMode contains IE version)
if (msie) {
  // IE logic here

  if (msie === 9) {
    // IE 9 logic here

  }
}

you should use conditional comments

<!--[if IE 9]>
<script type="text/javascript">
    window.isIE9 = true;
</script>
<![endif]-->

You can then check for $window.isIE9 in your controllers.