If `(sin^(-1)x+sin^(-1)y)(sin^(-1)Z+sin^(-1)w)=pi^(2)` and `n_(1),n_(2),n_(3),n_(4)` in N value of `|(x^(n1),y^(n2)),(z^(n)3,w^(n4))|` cannot be equal to

Options

A. `-2`
B. 0
C. 1
D. 2

Explanation

`sin^(-1)x+sin^(-1)` y are `pi` and `pi` respectively
`therefore (sin^(-1)+sin^(-1)y)(sin^(-1)z+sin^(-1)w)=pi^(2)`
or `(sin^(-1)x=sin^(-1)y=sin^(-1)z=sin^(-1)w=-(pi)/(2))`
`rarr x=y=z=w=1 or x=y=z=w=-1`
if x=y=z=w=1 then
hence `|{:(x^(n1), x^(n2)),(z^(n3) , w^(n4)):}|` connot be equal to 1