How can you handle difficult people at work ?

First investigate indepedently where the real problem is; is it you yourself or truly them? If it is you then yiu need to change for the better. If it is truly them; find out how difficult they are-extent, what makes them difficult or why they behave that way- is it bandwagon, is it personality, is it stress or personal problems, is it response to how they are treated, is it internal & or external pressure, is it financial- salaries or wages. Until you know the exact problem & cause you can never come up with the best solutions. Therefore if you have discovered where the problem is & what cause it; you can create an open minded dialogue with them or talk to their trusted friends to help mitigate, you can also involve professionals like pyschologists or counselors etc.

Talk to him politely and professionally, ask him what his problem is to be upset or difficult may be someone have told him something wrong or used bad word or may be he/she has a genuine reason such as someone is sick in his family?

The easiest way to defeat something is to embrace it and show them that you are difficult than them.. 

study about those workers and find the remedys