No TV-out connections on the Inspire, but if you have a DLNA-compatible TV, you can enable a connection to share the media between the Inspire and the TV. I pulled this off of the HTC site for Inspire Support:
What is Connected Media and how can I use it?
Connected Media is an application that when connected to a DLNA capable device or adaptor, allows you to output Music, Photos, and Videos on your device to an external player (example, TV). To use Connected Media: Enable the DLNA on the receiving device. Enable Wi-Fi on your device. Connect to the listing for your DLNA device. On the device, go to Home>All Apps>Connected Media and select the content to be output to the external device.
Hope that helps.