1. **State the problem:** Verify the trigonometric identity $$\frac{\csc \theta \cdot \tan \theta}{\sec \theta} = 1$$ and show the steps to prove it. 2. **Recall the definitions and formulas:** - $$\csc \theta = \frac{1}{\sin \theta}$$ - $$\tan \theta = \frac{\sin \theta}{\cos \theta}$$ - $$\sec \theta = \frac{1}{\cos \theta}$$ 3. **Substitute the definitions into the left-hand side (LHS):** $$\frac{\csc \theta \cdot \tan \theta}{\sec \theta} = \frac{\frac{1}{\sin \theta} \cdot \frac{\sin \theta}{\cos \theta}}{\frac{1}{\cos \theta}}$$ 4. **Simplify the numerator:** $$\frac{1}{\sin \theta} \cdot \frac{\sin \theta}{\cos \theta} = \frac{\cancel{1} \cdot \cancel{\sin \theta}}{\cancel{\sin \theta} \cdot \cos \theta} = \frac{1}{\cos \theta}$$ 5. **Rewrite the expression:** $$\frac{\frac{1}{\cos \theta}}{\frac{1}{\cos \theta}}$$ 6. **Divide the fractions:** $$\frac{1}{\cos \theta} \times \frac{\cos \theta}{1} = \cancel{\frac{1}{\cos \theta}} \times \cancel{\cos \theta} = 1$$ 7. **Conclusion:** The left-hand side simplifies to 1, which equals the right-hand side, so the identity is verified. **Final answer:** $$\frac{\csc \theta \cdot \tan \theta}{\sec \theta} = 1$$