8.
\(sinx=-1\Rightarrow x=-\dfrac{\pi}{2}+k2\pi\)
9.
\(cosx=-\dfrac{\sqrt{3}}{2}\Rightarrow x=\pm\dfrac{5\pi}{6}+k2\pi\)
10.
\(tan\left(3x-30^0\right)=-\dfrac{\sqrt{3}}{3}\Leftrightarrow3x-30^0=-30^0+k180^0\)
\(\Leftrightarrow x=k60^0\)
11.
\(2sin2x+1=0\Leftrightarrow sin2x=-\dfrac{1}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=-\dfrac{\pi}{6}+k2\pi\\2x=\dfrac{7\pi}{6}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{12}+k\pi\\x=\dfrac{7\pi}{12}+k\pi\end{matrix}\right.\)
12.
\(cos3x-cosx=0\Leftrightarrow cos3x=cosx\)
\(\Leftrightarrow\left[{}\begin{matrix}3x=x+k2\pi\\3x=-x+k2\pi\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=k\pi\\x=k\dfrac{\pi}{2}\end{matrix}\right.\)
