\(sin^23x-cos^24x=sin^25x-cos^26x\)
\(\Leftrightarrow2sin^23x-2cos^24x=2sin^25x-2cos^26x\)
\(\Leftrightarrow2sin^23x-1+1-2cos^24x=2sin^25x-1+1-2cos^26x\)
\(\Leftrightarrow-cos6x-cos8x=-cos10x-cos12x\)
\(\Leftrightarrow cos6x-cos12x+cos8x-cos10x=0\)
\(\Leftrightarrow sin9x.sin6x+sin9x.sin4x=0\)
\(\Leftrightarrow sin9x.\left(sin6x+sin4x\right)=0\)
\(\Leftrightarrow2sin9x.sin5x.cosx=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sin9x=0\\sin5x=0\\cosx=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{k\pi}{9}\\x=\dfrac{k\pi}{5}\\x=\dfrac{\pi}{2}+k\pi\end{matrix}\right.\)
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