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1)
pt$\Leftrightarrow \frac{1}{4}(3cosx+cos3x)cos3x+\frac{1}{4}(3sinx-sin3x)sin3x=cos^34x$
$\Leftrightarrow 3(cosx.cos3x+sinx.sin3x)+cos^23x-sin^23x=4cos^34x$
$\Leftrightarrow 3cos2x+cos6x=4cos^34x$
$\Leftrightarrow 3cos2x+4cos^32x-3cos2x=4cos^34x$
$\Leftrightarrow cos^32x=cos^34x\Leftrightarrow cos2x=cos4x\Leftrightarrow \left[ \begin{matrix} 2x=4x+k2\pi\\ 2x=-4x+k2\pi\end{matrix}{} \right.\Leftrightarrow \left[ \begin{matrix}x=-k\pi\\ x=\frac{k\pi}{3} \end{matrix}{} \right.(k\in Z)$
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