The correct answer is C. only at synchronous speed.
A synchronous motor is an AC electric motor that runs at a constant speed, synchronized with the frequency of the AC power supply. The speed of a synchronous motor is determined by the frequency of the AC power supply and the number of poles on the stator.
A synchronous motor can develop synchronous torque only at synchronous speed. This is because the magnetic field of the stator must be synchronized with the magnetic field of the rotor in order for the motor to produce torque. If the motor is running below synchronous speed, the magnetic field of the stator will be ahead of the magnetic field of the rotor, and the motor will produce a braking torque. If the motor is running above synchronous speed, the magnetic field of the stator will be behind the magnetic field of the rotor, and the motor will produce a driving torque.
Options A and B are incorrect because a synchronous motor can develop synchronous torque only at synchronous speed. Option D is incorrect because a synchronous motor can only develop synchronous torque at synchronous speed.