\(1+sinx-cos2x=0\)
\(\Leftrightarrow1+sinx-\left(1-2sin^2x\right)=0\)
\(\Leftrightarrow sinx\left(1+2sinx\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sinx=0\\sinx=-\frac{1}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=k\pi\\x=-\frac{\pi}{6}+k2\pi\\x=\frac{7\pi}{6}+k2\pi\end{matrix}\right.\)
\(sin3x-sinx+cos2x=0\)
\(\Leftrightarrow2cos2x.sinx+cos2x=0\)
\(\Leftrightarrow cos2x\left(2sinx+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos2x=0\\sinx=-\frac{1}{2}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\frac{\pi}{4}+\frac{k\pi}{2}\\x=-\frac{\pi}{6}+k2\pi\\x=\frac{7\pi}{6}+k2\pi\end{matrix}\right.\)
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