[tex] = \sf \large \frac{ \sec A - 1}{ \sec \: A + 1 } [/tex]
[tex] = \sf \large \frac{ \frac{1}{ \cos A - 1} }{ \frac{1}{ \cos A + 1 } } [/tex]
[tex] \sf \large \: = \frac{ \frac{1 - \cos A }{ \green{ \cancel{ \cos A}} }}{ \frac{1 + \cos A }{ \green{\cancel{ \cos A} }} }[/tex]
[tex] \sf \large = \frac{1 - \cos A }{1 + \cos A } [/tex]
-,-
