Question

số nghiệm của hàm số Cos2018x.Cosx=0 có bao nhiêu nghiệm trên [0;2π]

Answer 1

\(\Leftrightarrow\left[{}\begin{matrix}cosx=0\\cos2018x=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}+k\pi\\2018x=\dfrac{\pi}{2}+n\pi\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}+k\pi\\x=\dfrac{\pi}{4036}+\dfrac{n\pi}{2018}\end{matrix}\right.\)

\(0\le x\le2\pi\Rightarrow\left\{{}\begin{matrix}0\le\dfrac{\pi}{2}+k\pi\le2\pi\\0\le\dfrac{\pi}{4036}+\dfrac{n\pi}{2018}\le2\pi\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}0\le k\le1\\0\le n\le4035\end{matrix}\right.\)

Có \(2+4036=4038\) nghiệm