[tex]\frac{1 + sin(x)}{cos(x)} + \frac{cos(x)}{1 + sin(x)}[/tex]
[tex]\frac{[1 + sin(x)][1 +sin(x)]}{cos(x)[1 + sin(x)]} + \frac{cos(x)[cos(x)]}{cos(x)[1 + sin(x)]}[/tex]
[tex]\frac{1 + 2sin(x) + sin^{2}(x)}{cos(x)[1 + sin(x)]} + \frac{cos^{2}(x)}{cos(x)[1 + sin(x)]}[/tex]
[tex]\frac{1 + 2sin(x) + sin^{2}(x) + cos^{2}(x)}{cos(x)[1 + sin(x)]}[/tex]
[tex]\frac{1 + 2sin(x) + 1}{cos(x)[1 + sin(x)]}[/tex]
[tex]\frac{1 + 1 + 2sin(x)}{cos(x)[1 + sin(x)]}[/tex]
[tex]\frac{2 + 2sin(x)}{cos(x)[1 + sin(x)]}[/tex]
[tex]\frac{2[1 + sin(x)]}{cos(x)[1 + sin(x)]}[/tex]
[tex]\frac{2}{cos(x)}[/tex]
[tex]2sec(x)[/tex]
