Answer
$$\frac{1+\tan(-\theta)}{\tan(-\theta)}=1-\cot\theta$$
Work Step by Step
$$A=\frac{1+\tan(-\theta)}{\tan(-\theta)}$$
$$A=\frac{1}{\tan(-\theta)}+\frac{\tan(-\theta)}{\tan(-\theta)}$$
$$A=\frac{1}{\tan(-\theta)}+1$$
- Negative-angle Identity:
$$\tan(-\theta)=-\tan\theta$$
$$A=-\frac{1}{\tan\theta}+1$$
- Reciprocal Identity:
$$\cot\theta=\frac{1}{\tan\theta}$$
$$A=-\cot\theta+1$$
$$A=1-\cot\theta$$
