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



Write the following expression as a single trigonometric function or a power of a trigonometric function: (csc β * tan β) / sec β. Choose the correct answer from the options provided.

Learn how to simplify the trigonometric expression (csc β * tan β) / sec β into a single trigonometric function or power of a function. This solution involves using trigonometric identities to rewrite and simplify the expression. Ideal for high school students studying trigonometric identities.

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