How do you prove that torque is equal to p.e sin theta

The relevant formula is:

\bold \tau = \bold m \times \bold B

where \normalsize \tau = torque acting on the dipole, m is the dipole moment vector and B is the external magnetic field. The value for m for a dipole is pl, where p = the magnetic pole strength and l is the vector between the two poles (fropm south to north). Now if you know how to apply the cross product between vectors m and B you're there.