question_answer

If the function \[f(x)=\left\{ \begin{matrix}    x+{{a}^{2}}\sqrt{2}\sin x, & 0\le x\le \pi /4  \\    x\cot x+b, & \pi /4\le x<\pi /2  \\    b\sin 2x-a\cos 2x, & \pi /2\le x\le \pi   \\ \end{matrix} \right.\] is continuous in the interval \[[0,\pi ],\] then the values of (a, b) are

A)  (0, 0)                                       

B)  (1, 1)

C)  \[(-1,-1)\]                                  

D)  Both (A) and (B)

E)  None of these