Монгол Бодлогын Сан

$2\cos x=\sqrt{4+\sin 3x}\Leftrightarrow \left\{ % \begin{array}{l} \cos x\geq 0 \\ \sin (\fbox{a}\sin^2x-\fbox{b}\sin x-3)=0 \end{array}\right. \Leftrightarrow\\ \Leftrightarrow \left\{\begin{array}{l} \cos x\geq 0\\ \left[ % \begin{array}{l} \sin x=0 \\ \sin x=-\dfrac{1}{\fbox{c}} \\ \end{array} % \right. \\ \end{array} % \right.$ $\Leftrightarrow$ $\left\{ % \begin{array}{l} \cos x\geq 0 \\ \left[ % \begin{array}{l} x=\fbox{d}k\pi \\ x=(-1)^n\dfrac{\fbox{f}}{\fbox{e}}\pi+\fbox{g}n\pi \\ \end{array} % \right. \\ \end{array} % \right.$ $\Leftrightarrow$\\ $\Leftrightarrow$ $x=\fbox{h}k\pi, x=-\dfrac{\pi}{\fbox{i}}+\fbox{j}n\pi, k,n\in \mathbb Z.$