Solve `sin^(-1)x-cos^(-1)x=sin^(-1)(3x-2)`

Explanation

To solve the equation \( \sin^{-1} x - \cos^{-1} x = \sin^{-1} (3x - 2) \), we can follow these steps:

### Step 1: Rewrite the equation
We know that \( \cos^{-1} x = \frac{\pi}{2} - \sin^{-1} x \). Therefore, we can rewrite the equation as:
\[ \sin^{-1} x - \left(\frac{\pi}{2} - \sin^{-1} x\right) = \sin^{-1} (3x - 2) \]
This simplifies to:
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