Answer
$$\sec\theta\cot\theta\sin\theta=1$$
Work Step by Step
$$A=\sec\theta\cot\theta\sin\theta$$
- Quotient Identity:
$$\cot\theta=\frac{\cos\theta}{\sin\theta}$$
- Reciprocal Identity:
$$\sec\theta=\frac{1}{\cos\theta}$$
We replace these into $A$, and we have
$$A=\frac{1}{\cos\theta}\times\frac{\cos\theta}{\sin\theta}\times\sin\theta$$
After all the eliminations, we are left with
$$A=1$$