Write the following expression as a single trigonometric function or a power of a trigonometric function.
\[
\frac{\csc \beta \tan \beta}{\sec \beta}
\]
Choose the correct answer below.
1
$\frac{\sin \beta \cos \beta}{\cos \beta \sin \beta}$
$\tan ^{2} \beta$
$\frac{1}{\tan ^{2} \beta}$
Answer
Final Answer: \(\boxed{1}\)
Step 1 ：Write the given expression as: \(\frac{\csc \beta \tan \beta}{\sec \beta}\)
Step 2 ：Replace the trigonometric functions with their equivalent expressions in terms of sine and cosine. The cosecant function is the reciprocal of the sine function, the tangent function is the ratio of sine to cosine, and the secant function is the reciprocal of the cosine function. So, the expression becomes: \(\frac{\frac{1}{\sin \beta} \frac{\sin \beta}{\cos \beta}}{\frac{1}{\cos \beta}}\)
Step 3 ：Simplify the expression to get: \(1\)
Step 4 ：Final Answer: \(\boxed{1}\)
