Once you're restarted the mini, launch its System Preferences application, click the Displays preference, and utter joyous noises when you discover that 1920 by 1200 now appears when you choose Scaled in this preference. Select it and the mini's screen will fill your iMac's display when you choose Full Screen mode.
Now, the word of caution. If you leave your Mac mini set up this way and flip on the TV, the mini's display will not appear on the TV's screen. And it won't for good reason: The TV doesn't natively support the 1920 by 1200 resolution and so just shows a black screen. Therefore, before attempting to use your mini with your TV, screen share into it and choose 720p in the Displays system preference. All will then be right with the world (or at least with your HDTV).
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