Answer
$$\frac{\tan(-\theta)}{\sec\theta}=-\sin\theta$$
Work Step by Step
$$A=\frac{\tan(-\theta)}{\sec\theta}$$
- Negative-Angle Identity:
$$\tan(-\theta)=-\tan\theta$$
Replace into $A$:
$$A=\frac{-\tan\theta}{\sec\theta}$$
- Reciprocal Identity:
$$\sec\theta=\frac{1}{\cos\theta}$$
- Quotient Identity:
$$\tan\theta=\frac{\sin\theta}{\cos\theta}$$
Replace into $A$:
$$A=\frac{-\frac{\sin\theta}{\cos\theta}}{\frac{1}{\cos\theta}}$$
$$A=-\frac{\sin\theta\cos\theta}{1\times\cos\theta}$$
$$A=-\sin\theta$$
