If `sin^(-1)x+sin^(-1)y=pi/2,t h e n(1+x^4+y^4)/(x^2-x^2y^2+y^2)` is equal to 1 (b) 2 (c) `1/2` (d) none of these

Options

A. 1
B. 2
C. `(1)/(2)`
D. none of these

Answer

B

Explanation

`sin^(-1) x + sin^(-1) y = (pi)/(2)`
`rArr sin^(-1) = (pi)/(2) - sin^(-1) y`
`rArr sin^(-1) x = sin^(-1) sqrt(1 - y^(2))`
`rArr x^(2) + y^(2) = 1`
`rArr (1 + x^(4) + y^(4))/(x^(2) - x^(2) y^(2) + y^(2)) = (1 + (x^(2) + y^(2))^(2) - 2x^(2) y^(2))/(1 - x^(2) y^(2))`
`= (1 + 1 - 2x^(2) y^(2))/(1 -x^(2) y^(2)) = 2`