53.
ĐK: \(x\ne\dfrac{\pi}{2}+k\pi;x\ne\dfrac{\pi}{3}+k\pi\)
\(\dfrac{tanx-\sqrt{3}}{sin\left(x-\dfrac{\pi}{3}\right)}=0\)
\(\Leftrightarrow tanx=\sqrt{3}\)
\(\Leftrightarrow x=\dfrac{\pi}{3}+k\pi\left(l\right)\)
Vậy phương trình đã cho vô nghiệm.
54.
ĐK: \(x\ne\dfrac{\pi}{2}+k\pi\)
\(cos2x.tanx=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos2x=0\\tanx=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{4}+\dfrac{k\pi}{2}\left(tm\right)\\x=k\pi\left(tm\right)\end{matrix}\right.\)
55.
ĐK: \(x\ne\dfrac{\pi}{4}+\dfrac{k\pi}{2};x\ne-\dfrac{\pi}{2}-k\pi\)
\(tan2x=tan\left(\dfrac{\pi}{4}-x\right)\)
\(\Leftrightarrow2x=\dfrac{\pi}{4}-x+k\pi\)
\(\Leftrightarrow3x=\dfrac{\pi}{4}+k\pi\)
\(\Leftrightarrow x=\dfrac{\pi}{12}+\dfrac{k\pi}{3}\)
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