show that for an induction machine with electrically open rotor,the
generated electromagnetic torque is zero

I assume this is some sort of homework question?

Either way, if the rotor coil is an open circuit, it can't move a
current, so it can't generate a magnetic field and move against the
permanent magnet, so there is no torque.  I assume you are talking
about a DC motor.  But I'm not sure how you would prove this
mathematically.  Your question's a little vague, but I hope this
helps.