If `sin^(- 1)(x-(x^2)/2+(x^3)/4-.....)+cos^(- 1)(x^2-(x^4)/2+(x^6)/4-.....)=pi/2` for `0 lt |x| lt sqrt2` then `x=`

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

using `sin^(-1) x +cso^(-1) x=(pi)/(2)` in statement 1 we get
`x-(x^(2))/(2)+(x^(2))/(4)…=x^(2)-(x^(4))/(2)+x^(6))/(4)`
`rarr (x)/(1+(x)/(2))=(x^(2))/(1+x^(2))/(2)`
`rarr x(2+x^(2))=x^(2)(2+x)`
so statement -01 is true
LHS of statement 2 si meaningful if
`x^(2)+x ge 0 x^(32)+x+1ge0 and 0 le sqrt(x^(2)+x+1)le1`
`rarr x^(2)+xge0 and x^(2)+xle0 rarr x^(2)+x=0 rarr x=0`
`rarr x=-1`
clearly x=-1 satisfies the statement -1