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. ` (pi)/(2)`
B. `pi`
C. `2pi`
D. `4pi`
