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The number of integer x satisfying sin^(...

The number of integer `x` satisfying `sin^(-1)|x-2|+cos^(-1)(1-|3-x|)=pi/2` is (a) 1 (b) 2 (c) 3 (d) 4

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Verified by Experts

The correct Answer is:
B
`sin^(-1) |x -2| + cos^(-1) (1 - |3 -x|) = (pi)/(2)`
or `|x -2| = 1 -|3 -x|`
or `|x -2| + |3 -x| = |(x -2) + (3 -x)|`
or `(x -2) (3-x) le 0`
or `2 le x le 3`
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