Which of the following is the solution set of the equation `sin^-1 x = cos ^-1 x+ sin ^-1(3x-2)`

Options

A. `[0,1/3]`
B. `[1/3,2/3]`
C. `[0,2/3]`
D. none of these

Explanation

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

### Step 1: Rewrite the Equation
We start with the equation:
\[ \sin^{-1} x = \cos^{-1} x + \sin^{-1}(3x - 2) \]
Using the identity \( \cos^{-1} x = \frac{\pi}{2} - \sin^{-1} x \), we can rewrite the equation as:
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