Although it is highly recommended that you seek professional help and replace the cable when required to avoid any hazards, you can repair a broken connection on your own if the damage is not much. Sometimes cable gets broken and
Step 1: Identify the damage and gather supplies
Minor damage to the cable jacket can be fixed with a simple liquid electrical tape. Apply the liquid tape using a paintbrush and let it dry.
If the cable end that connects to tv is damaged, you can simply disconnect the cable, remove the connector by twisting off and replace with the new connector.
Most cables used for TV and internet connections are RG-6 coaxial cables with a quarter on an inch diameter, stocking your supplies keeping it in mind. You will need a wire cutter and cable trimmer with RG-6 setting, and support to kneel on so you do not spoil your pants. You would also require two F-F cable connectors, two twist-on F- connectors and a six-inch length of RG-6 cable with pre-installed connectors. (Note: a cable connector is something that has an internal thread and a wire protruding out of the centre to connect to another cable section and a cable adapter is something with an external thread on both sides, to connect two cable connectors with each other.)
Step 2: Using wire cutters and trimmers
Completely cut out the damaged part and strip off 12mm of the black jacket, fold back the braided insulation and expose the dielectric insulation layers. Pull back the dielectric sheet and trim off some leaving only 3mm intact. Now you have exposed the central conductor. (Do this stripping and exposing of layers to both ends that you will be reconnecting in next step)
Step 3: Plugging the connectors
Slip-on the twist on F-connectors at both ends and install it firmly. (If you do not know how to do it, read this article on how to install an F connector.). Now plug the connectors at both ends of the RG cable with pre-installed connectors.
Good job! You have successfully fixed the broken coaxial cable. Now you can enjoy your TV and internet connection.