Câu 26 :
ĐKXĐ : \(\cos x\ne-1\)
\(\Leftrightarrow x\ne\pi+2k\pi\)
Ta có : \(PT\Leftrightarrow\sin3x=0\)
\(\Leftrightarrow3x=k\pi\)
\(\Leftrightarrow x=\dfrac{k}{3}\pi\)
Mà \(2\pi\le x\le4\pi\)
\(\Rightarrow2\le\dfrac{k}{3}\le4\)
\(\Rightarrow6\le k\le12\)
\(\Rightarrow k\in\left\{6;7;8;9;10;11;12\right\}\)
Thay vào x ta được : \(x\in\left\{2\pi;\dfrac{7}{3}\pi;\dfrac{8}{3}\pi;3\pi;\dfrac{10}{3}\pi;\dfrac{11}{3}\pi;4\pi\right\}\)
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C25)
Pt\(\Leftrightarrow cosx=cos\left(\dfrac{\pi}{2}-2x\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}-2x+k2\pi\\x=2x-\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\)\(\left(k\in Z\right)\)\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{6}+\dfrac{k2\pi}{3}\left(1\right)\\x=\dfrac{\pi}{2}-k2\pi\left(2\right)\end{matrix}\right.\)\(\left(k\in Z\right)\)
Do \(x\in\left[-2\pi;\dfrac{\pi}{2}\right]\)\(\Rightarrow\left[{}\begin{matrix}-2\pi\le\dfrac{\pi}{6}+\dfrac{k2\pi}{3}\le\dfrac{\pi}{2}\\-2\pi\le\dfrac{\pi}{2}-k2\pi\le\dfrac{\pi}{2}\end{matrix}\right.\)\(\left(k\in Z\right)\)\(\Rightarrow\left[{}\begin{matrix}-\dfrac{13}{4}\le k\le\dfrac{1}{2}\\\dfrac{5}{4}\ge k\le0\end{matrix}\right.\)\(\left(k\in Z\right)\)\(\Rightarrow\left[{}\begin{matrix}k=\left\{-3;-2;-1;0\right\}\\k=\left\{1;0\right\}\end{matrix}\right.\)
Tại k=-3 thay vào (1)\(\Rightarrow x=-\dfrac{11\pi}{6}\)
Tại k=-2 thay vào (1)\(\Rightarrow x=-\dfrac{7\pi}{6}\)
Tại k=-1 thay vào (1)\(\Rightarrow x=-\dfrac{\pi}{2}\)
Tại k=0 thay vào (1)\(\Rightarrow x=\dfrac{\pi}{6}\)
Tại k=1 thay vào (2)\(\Rightarrow x=-\dfrac{3\pi}{2}\)
Tại k= 0 thay vào (2)\(\Rightarrow x=\dfrac{\pi}{2}\)
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