` -> sin x=cos 2x`

`-> cos (pi/2 -x)=cos (2x)`

`->` \(\left[ \begin{array}{l}\dfrac{\pi}{2}-x=2x+k2\pi \\\dfrac{\pi}{2}-x=-2x+k2\pi\end{array} \right.\) 

`->`  \(\left[ \begin{array}{l}-3x=-\dfrac{\pi}{2}+k2\pi \\x=\dfrac{\pi}{2}+k2\pi\end{array} \right.\) 

`->` \(\left[ \begin{array}{l}x=\dfrac{\pi}{6}-\dfrac{k2\pi}{3} \\x=\dfrac{\pi}{2}+k2\pi\end{array} \right.\) `(k\inZZ)`

TH1: 

`-pi/2<=pi/6-(2k pi)/3 <= pi/2`

`-> -pi/6-pi/2 <= (-2k pi)/3 <= -pi/6+pi/2`

`-> -1/4-3/4 <= -k <= -1/4+3/4`

`-> -1/2 <= k <= 1`

`->` `k \in{0;1)`

`->` `x=pi/6` hoặc `x=-pi/2` 

Th2: 

`-pi /2 <= pi/2 +k2 pi <= pi/2`

`-> -pi <= k2pi <= 0`

`-> -1/2 <= k <=0`

`->` `k=0`

`->` `x=pi/2`

Vậy tổng tất cả các nghiệm là: `pi/6-pi/2+pi/2=pi/6`

`-> a=-1;b=6`

`-> a+b=5`