sin23x = cos22x
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![](https://rs.olm.vn/images/avt/0.png?1311)
\(\Leftrightarrow\sin^2x-\sin^22x+\sin^23x-\sin^24x=0\)
\(\Leftrightarrow\left(\sin x+\sin2x\right)\left(\sin2x-\sin x\right)+\left(\sin3x+\sin4x\right)\left(\sin4x-\sin3x\right)=0\)
\(\Leftrightarrow2\sin\dfrac{3}{2}x.\cos\dfrac{x}{2}.2\cos\dfrac{3}{2}x.\sin\dfrac{x}{2}+2\sin\dfrac{7}{2}x.\cos\dfrac{x}{2}.2\sin\dfrac{x}{2}\cos\dfrac{7}{2}x=0\)
\(\Leftrightarrow\sin3x.\sin x+\sin7x.\sin x=0\)
\(\Leftrightarrow\sin x\left(\sin3x+\sin7x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sin x=0\\\sin3x=\sin\left(-7x\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=k\pi\\3x=-7x+k2\pi\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=k\pi\\x=\dfrac{k\pi}{5}\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\Leftrightarrow1-cos6x-1-cos8x=1-cos10x-1-cos12x\)
\(\Leftrightarrow cos10x+cos12x-cos6x-cos8x=0\)
\(\Leftrightarrow cos11x.cosx+cos7x.cosx=0\)
\(\Leftrightarrow cosx\left(cos11x+cos7x\right)=0\)
\(\Leftrightarrow cosx.cos9x.cos2x=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=0\\cos2x=0\\cos9x=0\end{matrix}\right.\) \(\Leftrightarrow...\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2\sqrt{3}\sin^23x-cos6x=\sqrt{3}\\ \Leftrightarrow2sin^23x\left(\sqrt{3}+1\right)=\sqrt{3}+1\\ \Leftrightarrow sin^23x=\dfrac{1}{2}\Leftrightarrow\dfrac{1-cos6x}{2}=\dfrac{1}{2}\Rightarrow cos6x=0\Leftrightarrow x=\pm\dfrac{\pi}{12}+k\dfrac{\pi}{6}\left(k\in Z\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đáp án B
Ta có:
f ' x = 2 sin 3 x sin 3 x ' = 2 sin 3 x .3 c os 3 x = 3 sin 6 x .