Write the following expression as a single trigonometric function or a power of a trigonometric function.

StartFraction cosecant beta tangent beta Over secant beta EndFractioncscβ tanβsecβ

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Part 1

Choose the correct answer below.

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

Write the following expression as a single trigonometric function or a power of a trigonometric function. StartFraction cosecant beta tangent beta Over secant beta EndFraction

Learn how to simplify the trigonometric expression (csc β * tan β) / sec β to a single trigonometric function. This problem covers key trigonometric concepts, including identities and simplification techniques, and is ideal for high school students in Grades 10-12.

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