5.
ĐKXĐ: \(cos\left(x-30^0\right)\ne0\Leftrightarrow x\ne120^0+k180^0\)
Pt tương đương:
\(\left[{}\begin{matrix}tan\left(x-30^0\right)=0\\cos\left(2x-150^0\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-30^0=k180^0\\2x-150^0=90^0+k180^0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=30^0+k180^0\\x=120^0+k90^0\end{matrix}\right.\)
Kết hợp ĐKXĐ: \(\Rightarrow x=30^0+k180^0\)
6.
\(\Leftrightarrow2\sqrt{2}sinx.cosx+2cosx=0\)
\(\Leftrightarrow2cosx\left(\sqrt{2}sinx+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=0\\sinx=-\dfrac{\sqrt{2}}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}+k\pi\\x=-\dfrac{\pi}{4}+k2\pi\\x=\dfrac{5\pi}{4}+k2\pi\end{matrix}\right.\)
5. \(\Leftrightarrow\left[{}\begin{matrix}\tan\left(x-30\right)=0\\\cos\left(2x-150\right)=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x-30=360k\\\left[{}\begin{matrix}2x-150=90+360k\\2x-150=270+360k\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=30+360k\\x=120+180k\\x=210+180k\end{matrix}\right.\)
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6, \(\Leftrightarrow2\sqrt{2}\sin x.\cos x+2\cos x=0\)
\(\Leftrightarrow\cos x\left(1+\sqrt{2}\sin x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\cos x=0\\\sqrt{2}\sin x+1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x=\dfrac{\pi}{2}+k2\pi\\x=\dfrac{3}{2}\pi+k2\pi\end{matrix}\right.\\x=-\dfrac{\pi}{4}+k2\pi\\x=\dfrac{7}{4}\pi+k2\pi\end{matrix}\right.\)
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