a.
\(cos\left(3x-60^0\right)=\dfrac{2}{\sqrt{3}}>1\) (ktm)
Vậy pt vô nghiệm
b.
\(tan3x=-\dfrac{1}{\sqrt{3}}\)
\(\Leftrightarrow3x=-\dfrac{\pi}{6}+k\pi\)
\(\Leftrightarrow x=-\dfrac{\pi}{18}+\dfrac{k\pi}{3}\)
c.
\(4cotx+\pi=0\)
\(\Leftrightarrow cotx=-\dfrac{\pi}{4}\)
\(\Leftrightarrow x=arccot\left(-\dfrac{\pi}{4}\right)+k\pi\)
d.
\(\sqrt{3}sinx-1=0\)
\(\Leftrightarrow sinx=\dfrac{\sqrt{3}}{3}\)
\(\Leftrightarrow\left[{}\begin{matrix}x=arcsin\left(\dfrac{\sqrt{3}}{3}\right)+k2\pi\\x=\pi-arcsin\left(\dfrac{\sqrt{3}}{3}\right)+k2\pi\end{matrix}\right.\)
e.
\(2cot3x=\sqrt{2}\)
\(\Leftrightarrow cot3x=\dfrac{\sqrt{2}}{2}\)
\(\Leftrightarrow3x=arccos\left(\dfrac{\sqrt{2}}{2}\right)+k\pi\)
\(\Leftrightarrow x=\dfrac{1}{3}arccot\left(\dfrac{\sqrt{2}}{2}\right)+\dfrac{k\pi}{3}\)
f.
\(sinx=\dfrac{\pi}{4}\)
\(\Leftrightarrow\left[{}\begin{matrix}x=arcsin\left(\dfrac{\pi}{4}\right)+k2\pi\\x=\pi-arcsin\left(\dfrac{\pi}{4}\right)+k2\pi\end{matrix}\right.\)
