Let's solve the problem step-by-step.

The given expression is: $\frac{\csc \beta \cdot \tan \beta}{\sec \beta}$

Step 1: Rewrite in terms of sine and cosine

Let's rewrite each trigonometric function in terms of $\sin \beta$ and $\cos \beta$:

1. $\csc \beta = \frac{1}{\sin \beta}$
2. $\tan \beta = \frac{\sin \beta}{\cos \beta}$
3. $\sec \beta = \frac{1}{\cos \beta}$

Substituting these into the expression, we get: $\frac{\frac{1}{\sin \beta} \cdot \frac{\sin \beta}{\cos \beta}}{\frac{1}{\cos \beta}}$

Step 2: Simplify the expression

Now, simplify by multiplying the terms in the numerator and dividing by the denominator: $= \frac{\frac{\sin \beta}{\sin \beta \cdot \cos \beta}}{\frac{1}{\cos \beta}}$