Chapter 5 - Trigonometric Identities - Section 5.1 Fundamental Identities - 5.1 Exercises - Page 201: 57

$$\cos\theta\csc\theta=\cot\theta$$

$$A=\cos\theta\csc\theta$$ - Reciprocal Identity: $$\csc\theta=\frac{1}{\sin\theta}$$ Replace this into $A$, we have $$A=\cos\theta\times\frac{1}{\sin\theta}$$ $$A=\frac{\cos\theta}{\sin\theta}$$ $$A=\cot\theta\hspace{1cm}\text{(Quotient Identity)}$$