It is proved that sin (α + β) + 2cos (α - β) cos α cos β = Cos2 α + Cos2 β

It is proved that sin (α + β) + 2cos (α - β) cos α cos β = Cos2 α + Cos2 β

This equation doesn't hold!
Let α = Π / 2 β = 0
be
Left = sin Π / 2 + cos Π / 2cos Π / 2cos0
=1
Right = cos Π + cos0
=-1+1
=0
Left ≠ right
The equation doesn't hold!