<=> \(5cos\left[2\left(x+\dfrac{\pi}{6}\right)\right]=4sin\left[\pi-\left(\dfrac{\pi}{6}+x\right)\right]-9\)
<=> \(5cos\left[2\left(x+\dfrac{\pi}{6}\right)\right]=4sin\left(\dfrac{\pi}{6}+x\right)-9\)
<=> \(5\left(1-2sin^2\left(x+\dfrac{\pi}{6}\right)\right)=4sin.\left(x+\dfrac{\pi}{6}\right)-9\)
<=> \(10sin^2\left(x+\dfrac{\pi}{6}\right)+4sin\left(x+\dfrac{\pi}{6}\right)-14=0\)
<=> \(\left[{}\begin{matrix}sin\left(x+\dfrac{\pi}{6}\right)=1\left(nhận\right)\\sin\left(x+\dfrac{\pi}{6}\right)=-\dfrac{7}{5}\left(loại\right)\end{matrix}\right.\)
Với : \(sin\left(x+\dfrac{\pi}{6}\right)=1\Leftrightarrow\left(x+\dfrac{\pi}{6}\right)=\dfrac{\pi}{2}+k2\pi\)
<=> \(x=\dfrac{\pi}{3}+k2\pi\left(k\in Z\right)\)
Vậy tập nghiệm của pt là:
\(S=\left(\dfrac{\pi}{3}+k2\pi,k\in Z\right)\)
