Cortana, like or dislike, it is the search engine for your computer. But Cortana does not need to take up so much of the task bar if you do not want it there.
To minimize Cortana to just its icon, right-click the task bar, go to CORTANA and select SHOW CORTANA ICON
Now the task bar has a nice, simple and small, Cortana icon
Click the Cortana icon and the Start Menu opens with the Cortana search bar
Troy @ TLC