If `x in[-1/2,1] then sin^(-1)(sqrt(3)/(2)x-1/2sqrt(1-x^(2)))`

Options

A. `sin^(-1)1/2 -sin^(-1)x`
B. `sin^(-1)x-(pi)/(6)`
C. `sin^(-1)x+(pi)/(6)`
D. none of these

Explanation

To solve the expression \( \sin^{-1}\left(\frac{\sqrt{3}}{2}x - \frac{1}{2}\sqrt{1 - x^2}\right) \) where \( x \in \left[-\frac{1}{2}, 1\right] \), we will follow these steps:

### Step 1: Simplify the expression inside the inverse sine function

We start with the expression:
\[ y = \frac{\sqrt{3}}{2}x - \frac{1}{2}\sqrt{1 - x^2} \]
...