Deduce the final equation by using the cos and sin theta

Considerer the collision between a moving particle of mass M1 and an initially stationary particle of mass M2, assume collision occurs at an angle θ defined by the initial trajectory of M1 and the line joining the mass centers at contact.

1- Calculate the momentum vectors before and after collision of particles.

2- Calculate the kinetic energy of the two particles before and after collision.

3- Deduce that the ratio of the kinetic energy (E2) acquired by M2 relative to the kinetic energy (El) of M1 is:

4- Show that for a constant value of θ this ratio is maximum for M1=M2.