Compton scattering derivation, please, please help

Hi everyone,I've joined this forum specially to get help for Compton effect derivation. I'm trying and trying but can't solve it. please anyone help, explain it in a really easy way.here's the derivation from a site:Consider a photon of frequency u1 and wavelength l1 strikes a stationary electron of rest mass mo. After collision the photon is scattered at an angle of q with its original line of action. While electron moves forward at an angle of f with its original direction. Energy of photon before collision = E1= hu1Energy of electron before collision = E2= moc2Energy of photon after collision = E1`= hu2Energy of electron after collision = E2` = mc2Since the collision between photon and electron is elastic. Therefore energy and momentum will be conserved.Total energy before collision = Total energy after collisionE1 E2= E1` E2`hu1 moc2= hu2 mc2hu1- hu2= mc2– moc2h(u1-u2) = c2(m – mo)……………….(1)momentum of photon before collision = h /l1Momentum of electron before collision = 0Momentum of photon after collision = h /l2Momentum of electron after collision = mvMOMENTUM EQUATION ALONG X-AXISh/l1 0 = h/l2Cosq mvCosfh/l1= h/l2Cosq mvCosf………….(2)MOMENTUM EQUATION ALONG Y-AXIs0 0 = h/l2Sinq (-mvSinf)h/l2Sinq-mvSinf= 0……………….(3)Solving (1) , (2) and (3), we get the following result:1/u2– 1/u1= h/moc2(1- Cosq) ………….(4)c(1/u2– 1/u1) = hc/moc2(1- Cosq)c/u2– c/u1= h/moc (1- Cosq)Butc/u=l,therefore,l2-l1= h/moc (1- Cosq)wherel2-l1= Compton’s shift in wavelengthh/moc is called Compton’s wavelength and its value is 2.426X10-12 m.CONCLUSIONThus the frequencyu2of scattered photon after the collision will be less than the original frequencyu1.------------------------so everything is clear but just from the step of solving eq 1,2, 3 .can anyone explain the missing steps? please help.

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