Peskin Schroeder: How to Derive Sin^2 Using Compton Relation?

[Sombrero]

Dear PF,

I have one question form Peskin Schroeder...could you pls help me
It is very simple question...
Since I don't know how to write formulas here I put my question in attachment.

Thank you very much.

 

[dextercioby]

Well just use the fact that $pk=m\omega$ and $pk'=m\omega'$ plus the Compton relation

$$\frac{1}{\omega}-\frac{1}{\omega'}=\frac{\cos\theta - 1}{m}$$

And you'll get that -sin^2 after using a bit of trigonometry.