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You might not be aware that the autofocus you use when looking through the viewfinder - the one where you can choose the single or group of AF points you want to use is NOT the same as what you're seeing when using autofocus while using Live View. It's Phase Detect vs. Contrast Detect that you get in Live View, which is much slower and cannot focus, if you will, on as small an area of a single phase detect AF site. The AF in Live View is, however available across the entire screen or very very close to it and is not limited to the restricted array of the AF points that light up in the viewfinder.
For landscape you're probably going to want to just use Live View manual focus and maybe get a Hoodman loupe to magnify and block out stray light. And if you're shooting landscape images at or near infinity, manual focus is lot more accurate anyway.