1.
\(2cos^2x-3cosx+1=0\)
\(\Leftrightarrow\left(cosx-1\right)\left(2cosx-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=1\\cosx=\dfrac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=k2\pi\\x=\pm\dfrac{\pi}{3}+k2\pi\end{matrix}\right.\)
7.
\(cos2x-5sinx-3=0\)
\(\Leftrightarrow1-2sin^2x-5sinx-3=0\)
\(\Leftrightarrow2sin^2x+5sinx+2=0\)
\(\Leftrightarrow\left(sinx+2\right)\left(2sinx+1\right)=0\)
\(\Leftrightarrow sinx=-\dfrac{1}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{3}+k2\pi\\x=\dfrac{4\pi}{3}+k2\pi\end{matrix}\right.\)
8.
ĐK: \(x\ne\dfrac{k\pi}{2}\)
\(5tanx-2cotx-3=0\)
\(\Leftrightarrow5tanx-\dfrac{2}{tanx}-3=0\)
\(\Leftrightarrow5tan^2x-3tanx-2=0\)
\(\Leftrightarrow\left(tanx-1\right)\left(5tanx+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}tanx=1\\tanx=-\dfrac{2}{5}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{4}+k\pi\\x=arctan\left(-\dfrac{2}{5}\right)+k\pi\end{matrix}\right.\)
2.
\(cos^2x+sinx+1=0\)
\(\Leftrightarrow1-cos^2x-sinx-2=0\)
\(\Leftrightarrow sin^2x-sinx-2=0\)
\(\Leftrightarrow\left(sinx+1\right)\left(sinx-2\right)=0\)
\(\Leftrightarrow sinx=-1\)
\(\Leftrightarrow x=-\dfrac{\pi}{2}+k2\pi\)
3.
\(2sin^2x+5sinx-3=0\)
\(\Leftrightarrow\left(sinx+3\right)\left(2sinx-1\right)=0\)
\(\Leftrightarrow sinx=\dfrac{1}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{3}+k2\pi\\x=\dfrac{2\pi}{3}+k2\pi\end{matrix}\right.\)
4.
ĐK: \(x\ne\dfrac{k\pi}{3}\)
\(cot^23x-cot3x-2=0\)
\(\Leftrightarrow\left(cot3x+1\right)\left(cot3x-2\right)=0\)
\(\Leftrightarrow cot3x=-1\)
\(\Leftrightarrow x=-\dfrac{\pi}{12}+\dfrac{k\pi}{3}\)
5.
\(2cos^2x+\sqrt{2}cosx-2=0\)
\(\Leftrightarrow\left(cosx+\sqrt{2}\right)\left(2cosx-\sqrt{2}\right)=0\)
\(\Leftrightarrow cosx=\dfrac{\sqrt{2}}{2}\)
\(\Leftrightarrow x=\pm\dfrac{\pi}{4}+k2\pi\)
6.
\(cos2x+cosx+1=0\)
\(\Leftrightarrow2cos^2x+cosx=0\)
\(\Leftrightarrow cosx\left(2cosx+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=0\\cosx=-\dfrac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}+k\pi\\x=\pm\dfrac{\pi}{3}+k2\pi\end{matrix}\right.\)
9.
\(sin^2\dfrac{x}{2}-2cos\dfrac{x}{2}+2=0\)
\(\Leftrightarrow cos^2\dfrac{x}{2}+2cos\dfrac{x}{2}-3=0\)
\(\Leftrightarrow\left(cos\dfrac{x}{2}-1\right)\left(cos\dfrac{x}{2}+3\right)=0\)
\(\Leftrightarrow cos\dfrac{x}{2}=1\)
\(\Leftrightarrow x=k2\pi\)
.Nhưng khoảng từ pi/2 đến -pi/4 thì vẫn bao gồm đáp án A mà sao mình lại chọn ạ
