To find the general solution of the equation \( \tan x = \sqrt{3} \), we can follow these steps:
### Step 1: Identify the reference angle
We know that \( \tan \frac{\pi}{3} = \sqrt{3} \). Therefore, the reference angle for our equation is:
\[
x = \frac{\pi}{3}
\]
### Step 2: Consider the periodic nature of the tangent function
The tangent function has a period of \( \pi \). This means that if \( x = \frac{\pi}{3} \) is a solution, then all solutions can be expressed in the form:
\[
x = \frac{\pi}{3} + n\pi
\]
where \( n \) is any integer.
### Step 3: Write the general solution
Thus, the general solution for the equation \( \tan x = \sqrt{3} \) is:
\[
x = \frac{\pi}{3} + n\pi, \quad n \in \mathbb{Z}
\]
### Summary
The general solution of \( \tan x = \sqrt{3} \) is:
\[
x = \frac{\pi}{3} + n\pi, \quad n \in \mathbb{Z}
\]
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To find the general solution of the equation \( \tan x = \sqrt{3} \), we can follow these steps:
### Step 1: Identify the reference angle
We know that \( \tan \frac{\pi}{3} = \sqrt{3} \). Therefore, the reference angle for our equation is:
\[
x = \frac{\pi}{3}
\]
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