7.
\(3cos^2x=-8cosx-5\)
\(\Leftrightarrow3cos^2x+8cosx+5=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=-1\\cosx=-\dfrac{5}{3}< -1\left(loại\right)\end{matrix}\right.\)
\(\Rightarrow x=\pi+k2\pi\)
8.
\(2sin^2x-3sinx+1=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sinx=1\\sinx=\dfrac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}+k2\pi\\x=\dfrac{\pi}{6}+k2\pi\\x=\dfrac{5\pi}{6}+k2\pi\end{matrix}\right.\)
\(\Rightarrow x=\dfrac{\pi}{6}\)
9.
\(sin^2x-4sinx=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sinx=0\\sinx=4>1\left(loại\right)\end{matrix}\right.\)
\(\Rightarrow x=k\pi\)
10.
\(2sin^2x+sinx-3=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sinx=1\\sinx=-\dfrac{3}{2}< -1\left(loại\right)\end{matrix}\right.\)
\(\Rightarrow x=\dfrac{\pi}{2}+k2\pi\)