Satement-1: if `1/2lexle1`then
`cos^(-1)x+cos^(-1){x/2+sqrt(3-3x^(2))/(2)}` is equal to `(pi)/(5)`
Statement-2: `sin^(-1)(2xsqrt(1-x^(2))=2sin^(-1)x if x in -(1)sqrt(2),(1)sqrt(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 given problem, we will analyze both statements step by step.

### Statement 1:
We need to verify if:
\[ \cos^{-1}(x) + \cos^{-1}\left(\frac{x}{2} + \frac{\sqrt{3 - 3x^2}}{2}\right) = \frac{\pi}{5} \]
for \( \frac{1}{2} \leq x \leq 1 \).
...