Решите уравнение: корень из 3 sin x + cos x=1

Решите задачу:

$\sqrt3sinx+cosx=1 |:\sqrt{(\sqrt{3)^{2}+1^{2}}}=2\\ \frac{\sqrt3}{2}sinx+\frac{1}{2}cosx=\frac{1}{2}\\ cos\frac{\pi}{6}sinx+sin\frac{\pi}{6}cosx=\frac{1}{2}\\ sin(\frac{\pi}{6}+x)=\frac{1}{2}\\ \frac{\pi}{6}+x=(-1)^{k}*\frac{\pi}{6}+{\pi}k\\ 1. \frac{\pi}{6}+x=\frac{\pi}{6}+2{\pi}k\\ 2. \frac{\pi}{6}+x}={\pi}-\frac{\pi}{6}+2{\pi}n\\ 1. x_1=2{\pi}k\\ 2. x_2=\frac{2\pi}{3}+2{\pi}n$