Ptrinh tương đương với:
$\sqrt2\sin x+\sqrt2\cos x+\dfrac{\sqrt2}{2}\sin x-\dfrac{\sqrt2}{2}\cos x=\dfrac{3\sqrt2}{2}$
$\to \sin x+\cos x+\dfrac{1}{2}\sin x-\dfrac{1}{2}\cos x=\dfrac{3}{2}$
$\to \dfrac{3}{2}\sin x+\dfrac{1}{2}\cos x=\dfrac{3}{2}$
$\to 3\sin x+\cos x=3$
$\to \sqrt{10}\sin(x+\alpha)=3$
$\to \sin(x+\alpha)=\dfrac{3}{\sqrt{10}}$
$\to \left[ \begin{array}{l}x=-\alpha+\arcsin\dfrac{3}{\sqrt{10}}+k2\pi \\x=-\alpha+\pi-\arcsin\dfrac{3}{\sqrt{10}}+k2\pi \end{array} \right.$
