How can I use a TV as a second monitor wirelessly (without a cable)?

Solution 1:

I assume that you are using a MacBook. If so, you can do it with an an Apple TV box, but since it works over WiFi, you will need to connect the AppleTV to the WiFi network. Use an HDMI cable to connect it to the TV. Then use Airplay on the McBook to connect wirelessly to the AppleTV and select "Use as separate display".

It would be much cheaper and easier to just use an HDMI dongle on the MacBook (mini display port, USB or USB-C depending on the model MacBook) and an HDMI cable to the TV.