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The image shows the mathematical expression \( \frac{1}{\sqrt{2}} \), which is often encountered in trigonometry, particularly when simplifying values of sine, cosine, or tangent for specific angles.

### Simplifying \( \frac{1}{\sqrt{2}} \):
To rationalize the denominator (remove the square root from the denominator), multiply both the numerator and the denominator by \( \sqrt{2} \):

\[
\frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2}
\]

Thus, the simplified form is \( \frac{\sqrt{2}}{2} \).

Would you like a more detailed explanation, or do you have any specific questions related to this expression?

Here are 5 related questions you might be interested in:
1. How is \( \frac{1}{\sqrt{2}} \) used in trigonometric functions like sine and cosine?
2. Why do we rationalize denominators in expressions involving square roots?
3. What are the common angles where \( \frac{1}{\sqrt{2}} \) appears in trigonometry?
4. How do you simplify other expressions with square roots in the denominator?
5. What is the geometric meaning of \( \frac{1}{\sqrt{2}} \) in terms of unit circle angles?

**Tip:** Rationalizing denominators is often done to make expressions easier to work with, especially in further calculations or integrations.

What is the simplified form of the mathematical expression \( \frac{1}{\sqrt{2}} \)?

Learn how to simplify the expression \( \frac{1}{\sqrt{2}} \), commonly encountered in algebra and trigonometry. This detailed step-by-step solution covers the concept of rationalizing denominators. Ideal for students in Grades 8-10.

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