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