Correct Answer - `(1)/(4sqrt2)`
`lim_(xto0)(sqrt2-sqrt(1+cosx))/(sin^(2)x)=lim_(xto0)(sqrt2-sqrt(2cos^(2)(x//2)))/((1-cos^(2)x))=lim_(xto0)(sqrt2(1-cos""(x)/(2)))/((1-cosx)(1+cosx))`
`=lim_(xto0)(sqrt2(1-cos""(x)/(2)))/((2sin^(2)""(x)/2)(1+cosx))=(1)/(sqrt2)lim_(xto0)((1-cos""(x)/(2)))/((1-cos^(2)""(x)/(2))(1+cosx))`
`=(1)/(sqrt2)lim_(xto0)(1)/((1+cos""(x)/(2))(1+cosx))=(1)/(sqrt2)xx(1)/((1+1)(1+1))=(1)/(4sqrt2).`
