Can a planet be on a stable orbit at a Lagrangian point of a binary star system?

Suppose we have a binary star system and a planet at the L4 or L5 point of the orbit of one of the stars around the other. The planet is thus illuminated by the two stars from the same distance and the angle between the stars is about 60 degrees. If the planet is tidally locked, it will be constantly illuminated by two non-moving stars. Is this possible?

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Can a planet be on a stable orbit at a Lagrangian point of a binary star system?

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