Simplify (cot(t)+tan(t))/(csc(-t))

$\frac{\cot (t) + \tan (t)}{\csc (- t)}$

Since $\csc (- t)$ is an odd function, rewrite $\csc (- t)$ as $- \csc (t)$ .

$\frac{\cot (t) + \tan (t)}{- \csc (t)}$