Step-by-step explanation:
[tex] \frac{1}{1 + \sin( \alpha ) } \frac{1}{1 - \sin( \alpha ) } \\ \frac{1 - \sin( \alpha ) + 1 + \sin( \alpha ) }{(1 + \sin( \alpha ))(1 - \sin( \alpha )) } \\ = \frac{2}{1 - {sin}^{2} \alpha } \\ \frac{2}{ {cos}^{2} \alpha } = 2 \: {sec}^{2} \alpha [/tex]
