cos(π/4) in fraction
Understand the Problem
The question is asking for the value of cos(π/4) expressed in fraction form. This involves recalling the cosine value of a common angle in trigonometry.
Answer
The value of $\cos\left(\frac{\pi}{4}\right)$ is $\frac{\sqrt{2}}{2}$.
Answer for screen readers
The value of $\cos\left(\frac{\pi}{4}\right)$ expressed in fraction form is $\frac{\sqrt{2}}{2}$.
Steps to Solve

Recall the cosine value for the angle
We need to recall the value of $\cos\left(\frac{\pi}{4}\right)$. This is a common angle in trigonometry. 
Recognize the special triangle
For the angle $\frac{\pi}{4}$, we can use the special 454590 triangle. In this triangle, both legs are of equal length, and the length of each leg can be considered as 1. The hypotenuse can be calculated as: $$ \text{Hypotenuse} = \sqrt{1^2 + 1^2} = \sqrt{2} $$ 
Calculate cosine
The cosine of an angle in a right triangle is given by the ratio of the adjacent side to the hypotenuse. For $\frac{\pi}{4}$: $$ \cos\left(\frac{\pi}{4}\right) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{1}{\sqrt{2}} $$ 
Rationalize the denominator
To express this in a more standard form, we multiply the numerator and the denominator by $\sqrt{2}$: $$ \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2} $$
The value of $\cos\left(\frac{\pi}{4}\right)$ expressed in fraction form is $\frac{\sqrt{2}}{2}$.
More Information
The cosine value of $\frac{\pi}{4}$ is commonly used in trigonometry, particularly in problems involving 45degree angles. This angle is significant because it has equal leg lengths in the special triangle, making calculations straightforward.
Tips
 Forgetting to rationalize the denominator when expressing $\frac{1}{\sqrt{2}}$.
 Mixing up the values of sine and cosine for the same angle.