Statement -1: If a is twice the tangent of the arithmetic mean of `sin^(-1)x and cos^(-1)` x , b the geometric mean of tanx and cot x then `x^(2)-ax+b=0rarr x=1` statement-2: `tan((sin^(-1)x+cos^(-1)x)/(2))=1`

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

It is given that
`a=2tan(sin^(-1)x+cos^(-1)x)/(2)and b=sqrt(tanx xx cot x)` ltrbgt `rarr a=2 tan(pi)/(4)=2 and b=1`
`therefore x^(2)-ax+b=0 rarr x^(2)-2x+1=0 rarr (x-1)^(2)=0 rarr x=-1 `
so statement 1 is true
`tan(sin^(-1)x+cos^(-1))/(2)=tan (pi)/(4)=1`
so statement -2 is also true