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Consider a function f defined by f(x)=si...

Consider a function f defined by `f(x)=sin^(-1) sin ((x+sinx)/2) AA x in [0,pi]`which satisfies `f(x)+f(2pi-x)=pi AA x in [pi, 2pi]` and `f(x)=f( 4pi-x)`for all `x in [2pi,4pi]` then If `alpha` is the length of the largest interval on which f(x) is increasing, then `alpha` =

A

`(beta)/(2)`

B

`beta`

C

`(beta)/(4)`

D

`2beta`

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The correct Answer is:
A
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