# Prove frac{cos(a)}{1+sin(a)}+(1+sin)

Prove $\frac{\mathrm{cos}\left(a\right)}{1+\mathrm{sin}\left(a\right)}+\left(1+\mathrm{sin}\right)$
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$\frac{\mathrm{cos}\left(a\right)}{1+\mathrm{sin}\left(a\right)}+\frac{1+\mathrm{sin}\left(a\right)}{\mathrm{cos}\left(a\right)}$
$=\frac{\left(1+\mathrm{sin}\left(a\right){\right)}^{2}+{\mathrm{cos}}^{2}\left(a\right)}{\left(1+\mathrm{sin}\left(a\right)\right)\mathrm{cos}\left(a\right)}$
$=\frac{\left(1+\mathrm{sin}\left(a\right){\right)}^{2}+1-{\mathrm{sin}}^{2}\left(a\right)}{\left(\left(1+\mathrm{sin}\left(a\right)\right)\mathrm{cos}\left(a\right)}$
$=\frac{2}{\mathrm{cos}\left(a\right)}=\frac{2}{\left(\frac{1}{\mathrm{sec}\left(a\right)}\right)=\frac{2}{\mathrm{sec}\left(a\right)}}$