If your laptop Mac stubbornly refuses to recognize the projector once you connect the two using the proper cabling and adapter, you may need to reset your System Management Unit and Non-Volatile RAM to clear out old or corrupt display settings.
Why wont my MacBook Pro detect an external display?
If you have an Apple adapter and your external display isnt working, try the following: Go to System Preferences > Display and try selecting a different resolution. If that still doesnt work, try restarting your Mac in safe mode and then reset the display resolution to defaults.
How do I change the HDMI settings on my Mac?
Connect your Mac to your TV If you need to adjust the resolution on your TV, choose Apple menu > System Preferences, click Displays, then click Display. Select “Default for display” to automatically use the best resolution, or select Scaled to manually select a resolution.