3.
\(cos3x=cosx\Rightarrow\left[{}\begin{matrix}3x=x+k2\pi\\3x=-x+k2\pi\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=k\pi\\x=k\dfrac{\pi}{2}\end{matrix}\right.\) \(\Rightarrow x=k\dfrac{\pi}{2}\)
4.
\(sin\left(4x-\dfrac{\pi}{3}\right)=\dfrac{1}{2}\Rightarrow\left[{}\begin{matrix}4x-\dfrac{\pi}{3}=\dfrac{\pi}{6}+k2\pi\\4x-\dfrac{\pi}{3}=\dfrac{5\pi}{6}+k2\pi\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{8}+k\dfrac{\pi}{2}\\x=\dfrac{7\pi}{24}+k\dfrac{\pi}{2}\end{matrix}\right.\)
5.
\(cosx=cos\dfrac{\sqrt{3}}{2}\)
\(\Rightarrow x=\pm\dfrac{\sqrt{3}}{2}+k2\pi\)
6.
\(\sqrt{3}+3tanx=0\)
\(\Leftrightarrow tanx=-\dfrac{\sqrt{3}}{3}\)
\(\Leftrightarrow x=-\dfrac{\pi}{6}+k\pi\)
7.
\(cotx=-\sqrt{3}\)
\(\Leftrightarrow x=-30^0+k180^0\)
