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