`sin(pi/3-sin^(-1)(-1/2))`is equal to (A) `1/2` (B) `1/3` (C) `1/4` (D) 1

Explanation

To solve the expression \( \sin\left(\frac{\pi}{3} - \sin^{-1}\left(-\frac{1}{2}\right)\right) \), we will follow these steps:

### Step 1: Find \( \sin^{-1}\left(-\frac{1}{2}\right) \)
The inverse sine function, \( \sin^{-1}(x) \), gives us the angle whose sine is \( x \). The range of \( \sin^{-1}(x) \) is from \( -\frac{\pi}{2} \) to \( \frac{\pi}{2} \).

To find \( \sin^{-1}\left(-\frac{1}{2}\right) \):
- We know that \( \sin\left(-\frac{\pi}{6}\right) = -\frac{1}{2} \).
- Therefore, \( \sin^{-1}\left(-\frac{1}{2}\right) = -\frac{\pi}{6} \).
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