To simplify the expression

$\frac{\csc \beta \cdot \tan \beta}{\sec \beta},$

we'll start by expressing each trigonometric function in terms of sine and cosine.

Step 1: Rewrite each trigonometric function

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

Step 2: Substitute these into the expression

Substituting these into the original expression gives:

$\frac{\csc \beta \cdot \tan \beta}{\sec \beta} = \frac{\frac{1}{\sin \beta} \cdot \frac{\sin \beta}{\cos \beta}}{\frac{1}{\cos \beta}}$

Step 3: Simplify the expression

Now, simplify each part:

[ = \frac{\frac{\sin \beta}{\sin \beta \cdot \cos \beta}}{\frac{1}{\cos \beta}} = \cos