Within Windows 10, the Cortana search box will be standardize on use of Edge and Bing standards for a consistant and more secure user experience.  Other search and browser standards will continue to be supported outside of Cortana 

https://blogs.windows.com/windowsexperience/2016/04/28/delivering-personalized-search-experiences-in-windows-10-through-cortana/

With Windows 10, we have invested in delivering comprehensive, end-to-end search capabilities that make Windows more personal, intuitive and helpful. The Cortana search box, in the bottom left of the Windows 10 taskbar, allows you to easily search across apps, documents, settings and the Web all with the help of your truly personal digital assistant.

Unfortunately, as Windows 10 has grown in adoption and usage, we have seen some software programs circumvent the design of Windows 10 and redirect you to search providers that were not designed to work with Cortana. The result is a compromised experience that is less reliable and predictable. The continuity of these types of task completion scenarios is disrupted if Cortana can’t depend on Bing as the search provider and Microsoft Edge as the browser. The only way we can confidently deliver this personalized, end-to-end search experience is through the integration of Cortana, Microsoft Edge and Bing – all designed to do more for you.

Of course, you can continue to use your search engine and browser of choice on Windows 10.  They can be accessed and used as you always have.  You can easily use our centralized default manager to choose your preferred default program for everything from browsing to email, and you can configure the search default setting in Microsoft Edge and Internet Explorer, which are available when you directly access those programs.