First question is does the tv do "all share cast" aka "screen mirroring".
The smart tv's only added the feature no more than 2 or 3 years ago. Post your model number and I'll check if you like.
I am assuming you have both devices on the same WiFi network.
On my tv, I just change the input to screen mirroring and it shows up the phone's list in the screen mirroring setting list.
There may be some settings on the tv that needs to be set, but I'll have to check later.
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Mogul --> Touch Pro --> EVO 4G --> Motorola Photon --> Galaxy S3 --> Galaxy S5