$3\sin x+2\cos x=1$
$\Rightarrow \dfrac{3}{\sqrt{11}}\sin x+\dfrac{2}{\sqrt {11}}\cos x=\dfrac{1}{\sqrt{11}}$
Đặt $\cos \alpha=\dfrac{3}{\sqrt{11}}$ và $\sin \alpha=\dfrac{2}{\sqrt{11}}$
Phương trình tương đương:
$\cos\alpha\sin x+\sin\alpha\cos x=\dfrac{1}{\sqrt{11}}$
$\Rightarrow \sin(x+\alpha)=\dfrac{1}{\sqrt{11}}$
$\Rightarrow \left[ \begin{array}{l} x+\alpha=\arcsin\dfrac{1}{\sqrt{11}}+k2\pi\\ x+\alpha=\pi-\arcsin\dfrac{1}{\sqrt{11}}+k2\pi \end{array} \right .$
$\Rightarrow \left[\begin{array}{l} x=-\alpha+\arcsin\dfrac{1}{\sqrt{11}}+k2\pi\\ x=-\alpha+\pi-\arcsin\dfrac{1}{\sqrt{11}}+k2\pi \end{array} \right .(k\in\mathbb Z)$
