Let f : (0, π) → R be a twice differentiable function such that
lim t→x (f(x) sint-f(t)sinx)/t-x= sin2x for all x∈(0,π)
If f(π/6)=-π/12, then which of the following statement(s) is (are) TRUE ?
(A) f(π/4)=π/4√2
(B) f(x)<x4/6-x2 for all x∈(0,π)
(C) There exists α∈(0,π) such that f '(α) = 0
(D) f ''(π/2)+f(π/2)=0