If `sin^(-1) x + sin^(-1)y = pi//2 and cos^(-1) x - cos^(-1) y = 0`, then value x and y respectively

Options

A. `(1)/(sqrt(2)),-(1)/(sqrt(2))`
B. `(1)/(2),(1)/(2)`
C. `(1)/(2), -(1)/(2)`
D. `(1)/(sqrt(2)),(1)/(sqrt(2))`

Answer

D

Explanation

Given, `sin^(-1)x + sin^(-1)y = (pi)/(2)" "...(i)`
and `cos^(-1)x-cos^(-1)y=0`
`rArr((pi)/(2)-sin^(-1)x)-((pi)/(2)-sin^(-1)y)=0`
`rArr sin^(-1)y-sin^(-1)x=0`
`rArr sin^(-1)y=sin^(-1)x" "...(ii)`
From equations (i) and (ii), we get
`2 sin^(-1)x = (pi)/(2)`
`rArr sin^(-1)x=(pi)/(4)`
`rArr x = (1)/(sqrt(2))`
From equation (ii)
`y = (1)/(sqrt(2))`