Xét ptrinh
$4 \sin x + \cos x = 4$
$\Leftrightarrow \dfrac{4}{\sqrt{17}} \sin x + \dfrac{1}{\sqrt{17}} \cos x = \dfrac{4}{\sqrt{17}}$
Đặt $\cos a = \dfrac{4}{\sqrt{17}}, \sin a = \dfrac{1}{\sqrt{17}}$. Khi đó, ptrinh trở thành
$\sin x \cos a + \sin a \cos x = \cos a$
$\Leftrightarrow \sin (x + a) = \cos a$
$\Leftrightarrow \sin (x + a) = \sin \left( \dfrac{\pi}{2} - a \right)$
$\Leftrightarrow x + a = \dfrac{\pi}{2} - a + 2k\pi$ hoặc $x + a = \dfrac{\pi}{2} + a + 2k\pi$
Vậy $x = \dfrac{\pi}{2} - 2a + 2k\pi$ hoặc $x = \dfrac{\pi}{2} + 2k\pi$
