Usually a good way to handle tailgaters is to:

Changing lanes to let a tailgater pass is considered a safe and effective way to deal with someone who is following too closely. This action creates more space between you and the tailgater, reducing the risk of a collision in the event of sudden stops or emergencies. It's important to prioritize safety and allow aggressive drivers to move past, rather than getting into a confrontation.

The other choices may seem like viable options in moments of frustration, but they can escalate a dangerous situation. Using a horn or making gestures can provoke aggressive behavior from the tailgater, increasing the risk of an accident. Speeding up might create more danger as it encourages risky driving behavior and does not solve the underlying issue of the tailgater's behavior. Ignoring the tailgater could lead to a potentially harmful scenario if they make a sudden move without awareness of your current speed or position.