Đk:\(x\ne\dfrac{k\pi}{2}\)
Pt\(\Leftrightarrow sin2x-cos2x=\dfrac{sinx}{cosx}+\dfrac{cosx}{sinx}\)
\(\Leftrightarrow sin2x-cos2x=\dfrac{1}{cosx.sinx}\)
\(\Leftrightarrow sin2x-cos2x=\dfrac{1}{\dfrac{1}{2}.sin2x}\)
\(\Leftrightarrow sin^22x-cos2x.sin2x=2\)
\(\Leftrightarrow sin^22x-cos2x.sin2x=2\left(sin^22x+cos^22x\right)\)
\(\Leftrightarrow-sin^22x-cos2x.sin2x-2cos^2x=0\) (vô nghiệm)
Vậy pt vô nghiệm
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