56.
ĐK: 
\(pt\Leftrightarrow\dfrac{sin^6x+cos^6x}{-tan\left(x-\dfrac{\pi}{4}\right).cot\left(x-\dfrac{\pi}{4}\right)}=-\dfrac{1}{4}\)
\(\Leftrightarrow sin^6x+cos^6x=\dfrac{1}{4}\)
\(\Leftrightarrow\left(sin^2x+cos^2x\right)\left(sin^4x+cos^4x-sin^2x.cos^2x\right)=\dfrac{1}{4}\)
\(\Leftrightarrow1-3sin^2x.cos^2x=\dfrac{1}{4}\)
\(\Leftrightarrow\dfrac{3}{4}sin^22x=\dfrac{3}{4}\)
\(\Leftrightarrow sin^22x=1\)
\(\Leftrightarrow\dfrac{1}{2}cos4x=-\dfrac{1}{2}\)
\(\Leftrightarrow x=\dfrac{\pi}{4}+\dfrac{k\pi}{2}\)
Đối chiếu điều kiện ta được \(x=-\dfrac{\pi}{4}+k\pi\)
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