How to know if you have broken tendon or ligament?

Function loss, defor. Most tendons perform a specified function. Loss of that function or deformity of the associated joint is likely the first indication of tendon or ligament injury.
Several ways. Tendons and ligaments don't break, they tear or cause avulsion injuries where they tear a piece of bone off the main portion of bone. X-ray, ultrasound, MRI will usually tell the story.