$\displaystyle tanxsinx + cosx = \frac{1}{cosx}$

$\displaystyle RS = \frac{1}{cosx}$

$\displaystyle = \frac{tanx}{sinx}$

$\displaystyle = \frac{sinx}{sinxcosx}$

$\displaystyle = \frac{sinxtanx}{sinxcosxtanx}$

$\displaystyle = \frac{sinxtanx}{sinxsinx}$

$\displaystyle = \frac{sinxtanx}{sin^2x}$

$\displaystyle = \frac{sinxtanx}{1 - cos^2x}$

What do I do from here? Is there a simpler way of solving this?