Match the following carefully

Options

A. `{:(a,b,c,d),(r,q,p,s):}`
B. `{:(a,b,c,d),(s,r,q,p):}`
C. `{:(a,b,c,d),(q,s,p,r):}`
D. `{:(a,b,c,d),(s,r,q,p):}`

Answer

C

Explanation

(a) `(sin^(-1) x)^(2) + (sin^(-1) y)^(2) = (pi^(2))/(2)`
`rArr (sin^(-1) x)^(2) = (sin^(-1) y)^(2) = (pi^(2))/(4)`
`rArr sin^(-1) x = +- (pi)/(2), sin^(-1) y = +- (pi)/(2)`
`rArr x = +- 1 and y = +- 1`
`rArr x^(3) + y^(3) = -2, 0, 2`
(b) `(cos^(-1) x)^(2) + (cos^(-1) y)^(2) = 2pi^(2)`
`rArr (cos^(-1) x)^(2) = (cos^(-1) y)^(2) = pi^(2)`
`rArr x = y = -1`
`rArr x^(5) + y^(5) = -1`
(c) `(sin^(-1) x)^(2) (cos^(-1) y)^(2) = (pi^(4))/(4)`
`rArr (sin^(-1) x)^(2) = (pi^(2))/(4) and (cos^(-1)y)^(2) = pi^(2)`
`rArr (sin^(-1)x) = +- (pi)/(2) and (cos^(-1) y) = pi`
`rArr x = +- 1 and y = -1`
`x -y = 0, 2`
(d) `|sin^(-1) x - sin^(-1) y| = pi`
`rArr sin^(-1) x = -(pi)/(2) and sin^(-1) y = (pi)/(2)`
`rArr x = -1 and y = 1`
or `sin^(-1) x = (pi)/(2) and sin^(-1) y = -(pi)/(2)`
`rArr x = 1 and y = -1`
`rArr x -y = -2, 2`