50.
ĐK: \(x\ne k\pi\)
\(sin3x.cotx=0\)
\(\Leftrightarrow sin3x.cosx=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sin3x=0\\cosx=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{k\pi}{3}\\x=\dfrac{\pi}{2}+k\pi\end{matrix}\right.\)
Đối chiếu điều kiện ta được \(x=\pm\dfrac{\pi}{3}+k\pi;x=\dfrac{\pi}{2}+k\pi\)
51.
ĐK: \(x\ne\dfrac{\pi}{8}+\dfrac{k\pi}{4};x\ne\dfrac{\pi}{4}+\dfrac{k\pi}{2}\)
\(tan4x-2tan2x=0\)
\(\Leftrightarrow\dfrac{2tan2x}{1-tan^22x}-2tan2x=0\)
\(\Leftrightarrow\dfrac{tan^32x}{1-tan^22x}=0\)
\(\Leftrightarrow tan2x=0\)
\(\Leftrightarrow x=\dfrac{k\pi}{2}\)
52.
ĐK: \(x\ne\dfrac{\pi}{2}+k\pi;x\ne\dfrac{\pi}{3}+k2\pi;x\ne\dfrac{2\pi}{3}+k2\pi\)
\(\dfrac{tan^2x-3}{2sinx-\sqrt{3}}=0\)
\(\Leftrightarrow tan^2x=3\)
\(\Leftrightarrow x=\pm\dfrac{\pi}{3}+k\pi\)
Đối chiều điều kiện ta được \(x=-\dfrac{2\pi}{3}+k2\pi;x=-\dfrac{\pi}{3}+k2\pi\)
