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If maximum and minimum values of |sin^(-...

If maximum and minimum values of `|sin^(-1)x|+|cos^(-1)x|` are M and m, then M+m is

A

`pi//2`

B

`pi`

C

`2pi`

D

`3pi`

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)={{:(sin^(-1)x+cos^(-1)x,,0le x le 1),(cos^(-1)x-sin^(-1)x,,-1le x le x lt 0):}`
`f(x)={{:(pi//2",",0le x le 1),((pi)/(2)-2sin^(1)x",",-1le x lt 0):}`
For `-1 le x le 0`
`-pi//2 le sin^(-1)x le 0`
`therefore -pi le 2 sin^(-1)x le 0`
`therefore 0 le -2 sin^(-1)x le pi`
`therefore pi//2 le pi//2 -2 sin^(-1) x le 3pi//2`
`therefore` Max. value `= 3pi//2`
and Min. value `= pi//2`
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