Simplify (1+cot(-theta))/(cot(-theta))

$\frac{1 + \cot (- θ)}{\cot (- θ)}$

Step 1

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

$\frac{1 - \cot (θ)}{\cot (- θ)}$

Step 2

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

$\frac{1 - \cot (θ)}{- \cot (θ)}$

Step 3

Move the negative in front of the fraction.

$- \frac{1 - \cot (θ)}{\cot (θ)}$