The set of values of k for which the equation `sin^(-1)x+cos^(-1)x +pi(|x|-2)=k pi` possesses real solution is [a,b] then the value of a + b is

Options

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

Answer

B

Explanation

`sin^(-1)x + cos(-1)x + pi(|x|-2)= k pi, x in [-1,1]`
`rArr (pi)/(2)+pi(|x|-2)= k pi`
`rArr (1)/(2)+|x|-2=k`
`rArr |x|=k + (3)/(2) in [0,1]`
`rArr 0 le k + (3)/(2) le 1`
`rArr -(3)/(2)le k le -(1)/(2)`