Removing the Search / Cortana box on the Task Bar in Windows 10
When you first upgrade to Windows 10, your Task Bar will include two new components – the search box (or Cortana if you’ve enabled this) and the Task View button next to it.
If, like me, you find it a little obtrusive, the good news is that it’s very easy to remove or minimise these buttons.
Simply right-click anywhere on the taskbar, select the Search menu, and select between the search box, just a search icon, or removing it altogether
From this same Task Bar menu you can also remove the Task View button if you wish
Incidentally, if you switch to using Small Icons on your task bar, as I do on my main laptop, (they’re a bit too small for a Surface) you only have the option of the icon or removing it altogether, which is a bit of a shame, as on my main laptop I actually have room for the extra search box, but like having the smaller icons