The given expression is:

\[
\frac{e^x}{\sec(x)} 
\]

Since \(\sec(x) = \frac{1}{\cos(x)}\), we can rewrite the expression as:

\[
\frac{e^x}{\frac{1}{\cos(x)}} = e^x \cdot \cos(x)
\]

Thus, the simplified form of the expression is:

\[
e^x \cos(x)
\]

Would you like a detailed explanation or any further steps, such as differentiation or integration?

Here are 5 questions related to this:

1. What is the derivative of \( e^x \cos(x) \)?
2. How would you integrate \( e^x \cos(x) \)?
3. What are the properties of the \(\sec(x)\) function?
4. How do the exponential and trigonometric functions interact in complex analysis?
5. How do you find critical points for the function \( f(x) = e^x \cos(x) \)?

**Tip**: When simplifying expressions involving trigonometric functions, consider using their reciprocal or other identities to rewrite them in more familiar forms.

Learn how to simplify the expression e^x/sec(x) using trigonometric identities. This solution involves the relationship between secant and cosine and demonstrates how to rewrite the given expression as e^x * cos(x). Suitable for students in Grades 11-12.

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