10.
\(cos2x-sinx+1=0\)
\(\Leftrightarrow2sin^2x+sinx-2=0\)
\(\Leftrightarrow sinx=\dfrac{-1+\sqrt{17}}{4}\)
\(\Leftrightarrow\left[{}\begin{matrix}x=arcsin\left(\dfrac{-1+\sqrt{17}}{4}\right)+k2\pi\\x=\pi-arcsin\left(\dfrac{-1+\sqrt{17}}{4}\right)+k2\pi\end{matrix}\right.\)
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8.
\(2sin^2x+sinx-3=0\)
\(\Leftrightarrow\left(sinx-1\right)\left(2sinx+3\right)=0\)
\(\Leftrightarrow sinx=1\)
\(\Leftrightarrow x=\dfrac{\pi}{2}+k2\pi\)
9.
\(cos^2x+2sinx-1=0\)
\(\Leftrightarrow-sin^2x+2sinx=0\)
\(\Leftrightarrow sinx\left(sinx-2\right)=0\)
\(\Leftrightarrow sinx=0\)
\(\Leftrightarrow x=k\pi\)
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