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These are tactics where one piece moves revealing another threat from the piece behind. In practice, they are often hard to spot and frequently devastating.
Double Check
Both pieces give a check on the King at the same time. This can be devastating; the only response is for the King to move more often into deeper trouble. It is so dangerous because blocking or attacking both pieces at once is not possible.
Discovered Attack
One piece moves uncovering a threat or attack from the piece behind. Although this revelaed threat is usually each to deal with, the real danger comes from the piece that has just moved.
Discovered Check
This is a more powerful form of discovered attack; the piece moves and uncovers a check from the piece behind. Since checks must be dealt with immediately, the piece that just moved has complete freedom of movement even into an otherwise vulnerable position.