Qs: Obviously:
This is my Codes:
I cannot simplify it to the expression as the right side of the equation.
This happens since the RHS is not equal to the LHS in the general case. It holds only for positive H
So
FullSimplify[ H^(1 - Sec[\[Beta]]) (H - s Sin[\[Beta]])^(-1 + Sec[\[Beta]]), Assumptions -> H > 0 ]
will return what you ask for.
Thanks.