Hi need help with energy, momentum and Compton effect, quantum mechanics? please

So the change in photon momentum is [(h / λ) - (h / (λ + ∆λ)]

So,
Before collision
Total horizontal momentum = (h/λ) + 0
Total vertical momentum = 0 + 0

After collision
Total horizontal momentum = [(h / λ) - (h / (λ + ∆λ)] cos Ѳ + m(e)v cos α
Total vertical momentum = [(h / λ) - (h / (λ + ∆λ)] sin Ѳ - m(e)v sin α

So, applying the conservation of momentum we get
Horizontally
(h / λ) = [(h / λ) - (h / (λ + ∆λ)] cos Ѳ + m(e)v cos α

Vertically

0 = [(h / λ) - (h / (λ + ∆λ)] sin Ѳ - m(e)v sin α
so,
m(e)v sin α = [(h / λ) - (h / (λ + ∆λ)] sin Ѳ

Hope you can follow this!