$\displaystyle tan+\frac{cos}{1+sin} = sec$

I've tried several ways again. This last one I tried multiplying by the complex conjugate but that led me nowhere near the answer I needed unless I messed up (shown below). I'm not gonna type all of the work I did because it's just too tedious doing the latex. I basically got the it down to:

$\displaystyle \frac {sin}{cos}$ $\displaystyle +$ $\displaystyle \frac{1-sin}{cos}$