$\displaystyle (1 + csc(-x))/(1 + sin(-x)) = sec(x) + tan(x)$
what do i do here? I keep forgetting my trig identities :/
On the right side:
$\displaystyle sec(x)+tan(x)$
$\displaystyle \frac{1}{cos(x)}+\frac{sin(x)}{cos(x)}$
$\displaystyle \frac{cos(x)+cos(x)sin(x)}{cos^{2}(x)}$
$\displaystyle \frac{cos(x)(1+sin(x)}{1-sin^{2}(x)}$
$\displaystyle \frac{cos(x)(1+sin(x)}{(1+sin(x))(1-sin(x))}$
$\displaystyle \frac{cos(x)}{1-sin(x)}$
$\displaystyle \frac{cos(x)}{1+sin(-x)}$
I'm a bit rusty on my trig as well, but maybe the above can help you. Got that errant cosine that you somehow need to manipulate. Work from the left hand side, and see if you get to any of the steps I did on the right hand side.