Direction: Given the function,
\(\rm f(x)=\left[\begin{matrix}x+a\sqrt2\sin x&0\le x<\frac{π}{4}\\\ 2x\cot x+b&\frac{π}{4}\le x<\frac{π}{2}\\\ a\cos2x-b\sin x&\frac{π}{2}\le x\leπ\end{matrix}\right.\) is continuous in [0, π], then
Find the value of a.
1
\(\frac{\pi}{6}\)
2
\(-\frac{\pi}{6}\)
3
\(\frac{\pi}{12}\)
4
\(-\frac{\pi}{12}\)