\(\Leftrightarrow4sin^23x.sin^2x=6+2sin3x\)
Do \(\left\{{}\begin{matrix}sin^23x\le1\\sin^2x\le1\end{matrix}\right.\) \(\Rightarrow VT\le4\)
\(sin3x\ge-1\Rightarrow VP=6+2sin3x\ge4\)
\(\Rightarrow VP\ge VT\)
Dấu "=" xảy ra khi và chỉ khi:
\(\left\{{}\begin{matrix}sin^23x=1\\sin^2x=1\\sin3x=-1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}sin^2x=1\\sin3x=-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}sin^2x=1\\3sinx-4sin^3x=-1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}sin^2x=1\\sinx\left(3-4sin^2x\right)=-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}sin^2x=1\\sinx=1\end{matrix}\right.\) \(\Leftrightarrow sinx=1\)
\(\Rightarrow x=\frac{\pi}{2}+k2\pi\)
