Chapter 14 - Trigonometric Identities and Equations - 14-1 Trigonometric Identities - Practice and Problem-Solving Exercises - Page 908: 30

$$1$$

Simplify $$\csc\theta\cos\theta\tan\theta.$$ Use the Reciprocal Identity $$\csc\theta=\frac{1}{\sin\theta}$$ and the Tangent Identity $$\tan\theta=\frac{\sin\theta}{\cos\theta}$$ to obtain $$\csc\theta\cos\theta\tan\theta=\bigg(\frac{1}{\sin\theta}\bigg)\cos\theta\bigg(\frac{\sin\theta}{\cos\theta}\bigg)=1.$$