My motherboard has this peculiarity: the HDMI display (television) is the primary output, and the DVI display (monitor) is the secondary output.
All desktop environments provide tools to configure the display layout: active heads, relative positions, etc. But to reach this feature, I have to go through the login screen first.
My problem is that I cannot see the television while I am sitting at the computer, and the login screen is displayed there. Thankfully, there is an easy workaround!