Match the following List I to List II

Answer

`a rarr s; b rarr p; c rarr q; d rarr r`

Explanation

`f(x) = sin^(-1) x + cos^(-1) x + cot^(-1)x = (pi)/(2) + cot^(-1) x, x in [-1, 1]`
For `x in [-1, 1], cot^(-1) x in [(pi)/(4), (3pi)/(4)]`
`rArr (pi)/(2) + cot^(-1) x in [(3pi)/(4) , (5pi)/(4)]`
(b) `f(x) = cot^(-1) x + tan^(-1) x + cosec^(-1) x`
`= (pi)/(2) + cosec^(-1) x, " where " x in (-oo, -1] uu [1, oo)`
Now `cosec^(-1) x in [-(pi)/(2), 0) uu (0, (pi)/(2)]`
`rArr (pi)/(2) + cosec^(-1) x in [0, (pi)/(2)) uu ((pi)/(2), pi]`
(c) `f(x) = cot^(-1) x + tan^(-1) x + cos^(-1) x`
`=(pi)/(2) + cos^(-1)x, " where " x in [-1, 1]`
`rArr (pi)/(2) + cos^(-1) x in [(pi)/(2), (3pi)/(2)]`
(d) `f(x) = sec^(-1) x + cosec^(-1) x + sin^(-1) x, " where " x in {-1, 1}`
`= (pi)/(2) + sin^(-1) x, " where " x in {-1, 1}`
Hence, `f(x) in {0, pi}`