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The set of values of k for which the eq...

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

A

0

B

`-2`

C

`-1`

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
`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)`
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