a: \(\Leftrightarrow1-2sin^2x-3sinx+2=0\)
\(\Leftrightarrow2sin^2x-3sinx-3=0\)
\(\Leftrightarrow sinx=\dfrac{3-\sqrt{33}}{4}\)
\(\Leftrightarrow\left[{}\begin{matrix}x=arcsin\left(\dfrac{3-\sqrt{33}}{4}\right)+k2\Pi\\x=\Pi-arcsin\left(\dfrac{3-\sqrt{33}}{4}\right)+k2\Pi\end{matrix}\right.\)
g: \(\Leftrightarrow1-sin^2x+sinx+1=0\)
\(\Leftrightarrow sin^2x-sinx-2=0\)
\(\Leftrightarrow sinx=-1\)
hay \(x=-\dfrac{\Pi}{2}+k2\Pi\)
`a)cos 2x-3sin x+2=0`
`<=>1-2sin^2 x-3sin x+2=0`
`<=>` $\left[\begin{matrix} sin x=\dfrac{-3+\sqrt{33}}{4}\\ sin x=\dfrac{-3-\sqrt{33}}{4} (VN)\end{matrix}\right.$
`<=>sin x=[-3+\sqrt{33}]/4`
`<=>` $\left[\begin{matrix} x=arc sin\dfrac{-3+\sqrt{33}}{4}+k2\pi\\ x=\pi-arc sin\dfrac{-3+\sqrt{33}}{4}+k2\pi\end{matrix}\right.$ `(k in ZZ)`
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`c)4 sin^2 2x-8cos^2 x+3=0`
`<=>4 sin^2 2x-(8cos^2 x -4)-1=0`
`<=>4(1-cos^2 2x)-4 cos 2x-1=0`
`<=>4-4cos^2 2x-4 cos 2x-1=0`
`<=>` $\left[\begin{matrix} cos x=\dfrac{1}{2}\\ cos x=\dfrac{-3}{2}(VN)\end{matrix}\right.$
`<=>cos x=1/2`
`<=>x=[+-\pi]/3+k2\pi` `(k in ZZ)`
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`e)cot^2` `x/2+4cot` `x/2+3=0`
`<=>` $\left[\begin{matrix} cot \dfrac{x}{2}=-1\\ cot \dfrac{x}{2}=-3\end{matrix}\right.$
`<=>` $\left[\begin{matrix} \dfrac{x}{2}=\dfrac{-\pi}{4}+k\pi\\ \dfrac{x}{2}=arc cot (-3)+k\pi\end{matrix}\right.$
`<=>` $\left[\begin{matrix} x=\dfrac{-\pi}{2}+k2\pi\\ x=2arc cot(-3)+k2\pi\end{matrix}\right.$ `(k in ZZ)`
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`g)cos^2 x+sin x+1=0`
`<=>1-sin^2 x+sin x+1=0`
`<=>` $\left[\begin{matrix} sin x=-1\\ sin x=-2 (VN)\end{matrix}\right.$
`<=>sin x=-1`
`<=>x=[-\pi]/2+k2\pi` `(k in ZZ)`
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