Find the value of x when tanx=1.

Explanation

To find the value of \( x \) when \( \tan x = 1 \), we can follow these steps:

### Step 1: Understand the Equation
We are given the equation:
\[ \tan x = 1 \]

### Step 2: Identify the Angle
We know that \( \tan \frac{\pi}{4} = 1 \). Therefore, we can rewrite the equation as:
\[ \tan x = \tan \frac{\pi}{4} \]

### Step 3: General Solution for Tangent
The general solution for the equation \( \tan x = \tan \alpha \) is given by:
\[ x = n\pi + \alpha \]
where \( n \) is any integer.

### Step 4: Substitute the Angle
Substituting \( \alpha = \frac{\pi}{4} \) into the general solution, we have:
\[ x = n\pi + \frac{\pi}{4} \]

### Step 5: Write the Final Answer
Thus, the values of \( x \) can be expressed as:
\[ x = n\pi + \frac{\pi}{4}, \quad n \in \mathbb{Z} \]