Windows 7, 8 and 10 are supposed to come with a small program that does exactly this: displayswitch.exe. This page lists the following parameters:
displayswitch.exe /internal Disconnect projector (same as "Show only on 1" from the Display Properties dialog)
displayswitch.exe /clone Duplicate screen
displayswitch.exe /extend Extend screen
displayswitch.exe /external Projector only (disconnect local) (same as "Show only on 2" from the Display Properties dialog)
For a one-click solution to the problem posed, simply create a *.bat-file containing the single line
call displayswitch.exe /extend
and save it to your desktop.
[I tested this on Windows 8.1, and it has been confirmed to work on Windows 10.]
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