How to Manage Cortana Settings in Windows
Cortana is always available on Windows, it means it can't be tuned off entirely. The Cortana must be integrated into Operating system to function well. Now many of the user do not want to use Cortana functions and for such case it should be better for them to hide Cortana from the taskbar.
Steps to Hide Cortana from Taskbar
RT click on search box and hover over Cortana, select Hidden from the side menu. This will remove search box from the taskbar.
You can review and control exactly what personal information Cortana can access by clicking into the search box and selecting Settings on the left pane. You can also search "Cortana settings" in the search box on the taskbar, and select Cortana & Search settings from the results.