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.