$\cos{x}+\sqrt3\sin{x}=\sqrt2$ হলে, x- এর মান কত?

$\frac{1}{2}\cos{x}+\frac{\sqrt3}{2}\sin{x}=\frac{1}{\sqrt2}\Rightarrow\cos{\left(x-\frac{\pi}{3}\right)}=\cos{\left(\frac{\pi}{4}\right)}\Rightarrow x-\frac{\pi}{3}=2n\pi\pm\frac{\pi}{4} \Rightarrow x=2n\pi+\frac{\pi}{12},\ 2n\pi+\frac{7\pi}{12}$

$\Rightarrow x=\left(24n+1\right)\frac{\pi}{12},\ \left(24n+7\right)\frac{\pi}{12}$