[tex]\frac{sec(\beta)-1}{1-cos(\beta)}=sec(\beta)[/tex]
we know that
[tex]sec(\beta)=\frac{1}{cos(\beta)}[/tex]
then, lets replace it
[tex]\frac{\frac{1}{cos(\beta)}-1}{1-cos(\beta)}=\frac{1}{cos(\beta)}[/tex]
multiple each member by [tex]cos(\beta)[/tex]
[tex]\frac{1-cos(\beta)}{1-cos(\beta)}=1[/tex]
simplifying
[tex]1=1[/tex]
