Statement -1: if `-1lexle1 then sin^(-1)(-x)=-sin^(-1)x and cos^(-1)(-x)=pi-cos^(-1)x` Statement-2: If `-1lexlex then cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))= 2cos^(-1)sqrt((1+x)/(2))`

Options

A. Statement-1 is is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Explanation

To solve the problem, we need to analyze both statements given in the question and determine their validity.

### Step 1: Analyze Statement 1
**Statement 1:** If \(-1 \leq x \leq 1\), then \(\sin^{-1}(-x) = -\sin^{-1}(x)\) and \(\cos^{-1}(-x) = \pi - \cos^{-1}(x)\).

1. **For \(\sin^{-1}(-x)\):**
- The sine function is an odd function, meaning \(\sin(-y) = -\sin(y)\).
- Therefore, \(\sin^{-1}(-x) = -\sin^{-1}(x)\) holds true for all \(x\) in the interval \([-1, 1]\).
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