[UPSC CSE 1996] Conservation Laws (Q50, 20M)

A particle of mass m_1 moving with a velocity v_1 undergoes an elastic collision with a particle of mass m_2 at rest, in laboratory-frame. After the collision the first particle moves at a certain angle to the direction of its initial velocity, and this angle is \theta in laboratory-frame and \phi in centre of mass-frame. If the ratio of masses \left(\frac{m_2}{m_1}\right) is a, show that \theta and \phi are related as \tan \phi = \left(\frac{\sin \phi}{\cos \phi + \frac{1}{A}}\right).