I've recently enabled FileVault on my OS X Yosemite install, everything went well at first, then it came to restarting my Mac to complete installation and this is where I hit a snag. My laptop is always in clamshell mode when I'm working from home, so naturally I rely on having everything displayed on the external monitor. With FileVault, after the laptop boots up, you're asked for a password, at this point even if your external monitor is plugged in, you will not get anything displayed on it. The laptop will sit waiting for you to open it up and type in your password before it continues to boot.
My monitor was connected via mini-DP, however when I tried the same using a HDMI cable, I also couldn't get a picture displayed on the external monitor.
This happens because at the point where FileVault is asking for a password, OS X hasn't booted yet. I'm guessing the pre-boot environment doesn't have the necessary drivers to output to an external monitor.
After reading a little online about this issue, it appears to be new in Yosemite and it was possible to get external monitor display working on previous versions of OS X. As far as I know there is no known workaround or fix for this other than disabling FileVault.
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