The principal value of `tan^(-1)sqrt(3)` is `"……."`

Explanation

To find the principal value of \( \tan^{-1}(\sqrt{3}) \), we can follow these steps:

### Step 1: Set up the equation
Let \( \theta = \tan^{-1}(\sqrt{3}) \). This means that:
\[ \tan(\theta) = \sqrt{3} \]

### Step 2: Identify the angle
We need to find the angle \( \theta \) such that the tangent of that angle equals \( \sqrt{3} \). From trigonometric values, we know:
\[ \tan\left(\frac{\pi}{3}\right) = \sqrt{3} \]
This indicates that \( \theta = \frac{\pi}{3} \).

### Step 3: Verify the range
The range of the \( \tan^{-1} \) function is \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \). Since \( \frac{\pi}{3} \) (which is approximately 1.047 radians) lies within this range, it is a valid principal value.

### Conclusion
Thus, the principal value of \( \tan^{-1}(\sqrt{3}) \) is:
\[ \frac{\pi}{3} \]

### Final Answer
The principal value of \( \tan^{-1}(\sqrt{3}) \) is \( \frac{\pi}{3} \).

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