Giải thích các bước giải:
Ta có:
\[\begin{array}{l}
4{\sin ^2}x + 6\sqrt 3 \sin x.\cos x + 2{\cos ^2}x = 4\\
\Leftrightarrow 4{\sin ^2}x + 6\sqrt 3 \sin x.\cos x + 2{\cos ^2}x = 4\left( {{{\sin }^2}x + {{\cos }^2}x} \right)\\
\Leftrightarrow 6\sqrt 3 \sin x.\cos x - 2{\cos ^2}x = 0\\
\Leftrightarrow 3\sqrt 3 \sin x.\cos x - {\cos ^2}x = 0\\
\Leftrightarrow \cos x\left( {3\sqrt 3 \sin x - \cos x} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\cos x = 0\\
3\sqrt 3 \sin x = \cos x
\end{array} \right.\\
{\sin ^2}x + {\cos ^2}x = 1 \Leftrightarrow {\sin ^2}x + {\left( {3\sqrt 3 \sin x} \right)^2} = 1\\
\Leftrightarrow 28{\sin ^2}x = 1\\
\Leftrightarrow {\sin ^2}x = \frac{1}{{28}}
\end{array}\]
