Ngân hàng bài tập
B
Giải phương trình \(\cos2x\cdot\tan x=0\).
 | \(x=k\dfrac{\pi}{2}\,(k\in\mathbb{Z})\) |
 | \(\left[\begin{array}{l}x=\dfrac{\pi}{2}+k\pi\\ x=k\pi\end{array}\right.\,(k\in\mathbb{Z})\) |
 | \(\left[\begin{array}{l}x=\dfrac{\pi}{4}+k\dfrac{\pi}{2}\\ x=k\pi\end{array}\right.\,(k\in\mathbb{Z})\) |
 | \(x=\dfrac{\pi}{2}+k\pi\,(k\in\mathbb{Z})\) |
1 lời giải
Chọn phương án C.
\(\begin{aligned}
\cos2x\cdot\tan x=0\Leftrightarrow&\left[\begin{array}{l}\cos2x=0\\ \tan x=0\end{array}\right.\\
\Leftrightarrow&\left[\begin{array}{l}2x=\dfrac{\pi}{2}+k\pi\\ x=k\pi\end{array}\right.\\
\Leftrightarrow&\left[\begin{array}{l}x=\dfrac{\pi}{4}+k\dfrac{\pi}{2}\\ x=k\pi\end{array}\right.\,(k\in\mathbb{Z})
\end{aligned}\)