The solution set of the equation
`cos^(-1)x-sin^(-1)x=sin^(-1)(1-x)` is

Options

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

Explanation

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

### Step 1: Understand the Domain
The functions \( \cos^{-1}x \) and \( \sin^{-1}x \) are defined for \( x \) in the interval \([-1, 1]\). However, we need to check the conditions for both sides of the equation.

### Step 2: Analyze the Left-Hand Side (LHS)
The LHS is \( \cos^{-1}x - \sin^{-1}x \). We know that:
\[
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