Statement-1:`sin^(-1)tan((tan^(-1))x+tan^(-1)(1-x))]` `=(pi)/(2)` has no non zero integral solution Statement-2: The greatest and least values of `(sin^(-1)x)^(3)+(cos^(-1)x)^(3) are (7pi)^(3)/(8) and (pi)^(3)/(32)` respectively

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

`sin^(-1)[tan (tan^(-1)x+tan^(-1)(1-x))]=(pi)/(2)`
`rarr sin^(-1)[tan{tan^(-1)(x+1-x)/(1-x(1-x))}] =(pi)/(2)`
`rarr tan{ tan^(-1)(1)/(1-x+x^(2))}=1`
` rarr (1)/(1-x+x^(2))=1 rarr x^(2)-x+1=1 rarr x=0 0,1`
so statement 1 is not true
statement 2 si true