The Principal value of `Cos^(-1) (sqrt(3)/(2))` is :

Options

A. `(pi)/(8)`
B. `(pi)/(6)`
C. `(pi)/(3)`
D. None of these

Answer

To find the principal value of \( \cos^{-1} \left( \frac{\sqrt{3}}{2} \right) \), we can follow these steps:

### Step 1: Identify the angle whose cosine is \( \frac{\sqrt{3}}{2} \).

We know from trigonometric values that:
\[ \cos \left( \frac{\pi}{6} \right) = \frac{\sqrt{3}}{2} \]

### Step 2: Apply the inverse cosine function.

Using the property of the inverse cosine function, we can write:
\[ \cos^{-1} \left( \frac{\sqrt{3}}{2} \right) = \frac{\pi}{6} \]

### Step 3: Verify the range of the inverse cosine function.

The range of the principal value of \( \cos^{-1} x \) is \( [0, \pi] \). Since \( \frac{\pi}{6} \) falls within this range, it confirms that our solution is valid.

### Conclusion:

Thus, the principal value of \( \cos^{-1} \left( \frac{\sqrt{3}}{2} \right) \) is:
\[ \frac{\pi}{6} \]

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