The function $f(x)=\left\{\begin{array}{1 1}x+a\sqrt 2\sin x&0\leq x < \large\frac{\pi}{4}\\2x\cot x+b&\large\frac{\pi}{4}\normalsize \leq x < \frac{\pi}{2}\\a\cos 2x-b\sin x&\large\frac{\pi}{2}\normalsize < x \leq \pi\end{array}\right.$ is continuous for $0 \leq x \leq \pi$ then a,b are

Question

$\begin{array}{1 1}(a)\;\large\frac{\pi}{6},\frac{\pi}{12}&(b)\;\large\frac{\pi}{3},\frac{\pi}{6}\\(c)\;\large\frac{\pi}{6},-\frac{\pi}{12}&(d)\;\text{None of these}\end{array}$