[tex] \frac{ \cos(x) }{1 + \sin(x) } + \frac{ \sin(x) }{ \cos(x) } \\ = \frac{ \cos(x) \times \cos(x) }{(1 + \sin(x))( \cos(x) ) } + \frac{ \sin(x) \times (1 + \sin(x) }{ \cos(x) \times (1 + \sin(x)) } \\ = \frac{ { \ { \cos(x) }^{2} + sin(x) }^{2} + \sin(x) }{(1 + \sin(x))( \cos(x)) } \\ \frac{1 + \sin(x) }{(1 + \sin(x)) ( \cos(x)) } \\ = \frac{1}{ \cos(x) } \\ = \sec(x) [/tex]
Remember to use theta not x, and cos^2+sin^2=1
