Simplify (1-tan(-theta))/(tan(-theta))

$\frac{1 - \tan (- θ)}{\tan (- θ)}$

Simplify the numerator.

Since $\tan (- θ)$ is an odd function, rewrite $\tan (- θ)$ as $- \tan (θ)$ .

$\frac{1 - - \tan (θ)}{\tan (- θ)}$

Multiply $- - \tan (θ)$ .

Multiply $- 1$ by $- 1$ .

$\frac{1 + 1 \tan (θ)}{\tan (- θ)}$

Multiply $\tan (θ)$ by $1$ .

$\frac{1 + \tan (θ)}{\tan (- θ)}$

Since $\tan (- θ)$ is an odd function, rewrite $\tan (- θ)$ as $- \tan (θ)$ .

$\frac{1 + \tan (θ)}{- \tan (θ)}$

Move the negative in front of the fraction.

$- \frac{1 + \tan (θ)}{\tan (θ)}$