ĐK: \(x\ne\dfrac{\pi}{2}+k\pi\)
\(\dfrac{4sin^22x+6sin^2x-9-3cos2x}{cosx}=0\)
\(\Leftrightarrow4sin^22x+6sin^2x-9-3cos2x=0\)
\(\Leftrightarrow4\left(sin^22x-1\right)+3\left(2sin^2x-1\right)-3cos2x-2=0\)
\(\Leftrightarrow-4cos^22x-3cos2x-3cos2x-2=0\)
\(\Leftrightarrow2cos^22x+3cos2x+1=0\)
\(\Leftrightarrow\left(2cos2x+1\right)\left(cos2x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos2x=-\dfrac{1}{2}\\cos2x=-1\end{matrix}\right.\)
Với \(cos2x=-\dfrac{1}{2}\Leftrightarrow2x=\pm\dfrac{2\pi}{3}+k2\pi\Leftrightarrow x=\pm\dfrac{\pi}{3}+k\pi\left(tm\right)\)
Với \(cos2x=-1\Leftrightarrow2x=\dfrac{\pi}{2}+k2\pi\Leftrightarrow x=\dfrac{\pi}{4}+k\pi\left(tm\right)\)
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