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The difference between the greatest and the least values of the function `f(x)=sin2x-x` on `[-pi/2 ,pi/2]`

A

`pi`

B

`(sqrt(3)-(pi)/(3))`

C

`(sqrt(3))/(2)+(pi)/(3)`

D

`-(sqrt(3))/(2)+(2pi)/(3)`

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The correct Answer is:
A
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