Prove that: `3sin^(-1)x=sin^(-1)(3x-4x^3), x in [-1/2,1/2]`

Explanation

To prove that \( 3\sin^{-1}x = \sin^{-1}(3x - 4x^3) \) for \( x \in \left[-\frac{1}{2}, \frac{1}{2}\right] \), we can follow these steps:

### Step 1: Let \( \theta = \sin^{-1}x \)

This implies that:
\[ \sin \theta = x \]
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