Let we have a function g(x) = √ (1-x) / (1+x) - ( log(1+x) / sin-1x )
Now g(1) = 0 - log(2) / (π/2) = -2 * 0.301 / π = -0.602 / π
g(0) = 1 - Limx --> 0 [(1/1+x)] / [1 / sqrt(1 - x2)]
= 1 - 1 = 0
Now as it is clear that :
g(0) > g(1) hence it is decreasing function and max value is at x = 0..
Thus g(x) < 0 always for 0 < x < 1 [ Equality holds at x = 0 ]
Thus ,
√ (1-x) / (1+x) - ( log(1+x) / sin-1x ) < 0
==> √ (1-x) / (1+x) < log(1+x) / sin-1x
And on verification at points 0 and 1 , we will find each of them cant exceed the value of 1..
Hence A) should be the correct option..