https://file.aiquickdraw.com/mathbot/file/1726931112031c4kunszi.jpg

The expression in the image you uploaded is:

\[
\frac{\sec\theta}{\sqrt{\sec^2\theta - 1}}
\]

To simplify this, we can use a trigonometric identity:

\[
\sec^2\theta - 1 = \tan^2\theta
\]

Thus, the expression becomes:

\[
\frac{\sec\theta}{\sqrt{\tan^2\theta}} = \frac{\sec\theta}{|\tan\theta|}
\]

Therefore, the simplified form of the expression is:

\[
\frac{\sec\theta}{|\tan\theta|}
\]

Would you like to explore further, or ask for details on how this simplification works?

Here are some related questions for practice:

1. What is the relationship between \(\sec\theta\) and \(\cos\theta\)?
2. How can you express \(\tan\theta\) in terms of \(\sin\theta\) and \(\cos\theta\)?
3. Can you apply this identity \(\sec^2\theta - 1 = \tan^2\theta\) in other trigonometric expressions?
4. What happens if \(\theta = 0\)? Is the expression valid?
5. How can you graph the original expression and its simplified form?

**Tip:** Understanding trigonometric identities can make simplifying expressions much easier. Familiarize yourself with the key ones!

Simplify the expression \( \frac{\sec\theta}{\sqrt{\sec^2\theta - 1}} \)

Learn how to simplify the trigonometric expression \( \frac{\sec\theta}{\sqrt{\sec^2\theta - 1}} \) using trigonometric identities. This example demonstrates the application of the identity \( sec^2(θ) - 1 = tan^2(θ) \), suitable for students in Grades 10-12.

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