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Toán Lớp 11: tan$^{3}$x + 2tanx + 3 = $\frac{3}{cos^{2}x}$

Home/ Toán Lớp 11: tan$^{3}$x + 2tanx + 3 = $\frac{3}{cos^{2}x}$

Toán Lớp 11: tan$^{3}$x + 2tanx + 3 = $\frac{3}{cos^{2}x}$

Trang Tháng Bảy 14, 2022 Toán học 1 Comment 0 views

Toán Lớp 11: tan$^{3}$x + 2tanx + 3 = $\frac{3}{cos^{2}x}$

Comments ( 1 )

thienthanh
14 Tháng Bảy, 2022 at 7:50 chiều

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~rai~

\(\tan^3x+2\tan x+3=\dfrac{3}{\cos^2x}\quad\left(x\ne \dfrac{\pi}{2}+m\pi;m\in\mathbb{Z}\right)\\\Leftrightarrow\tan^3x+2\tan x+3=3(1+\tan^2x)\\\Leftrightarrow \tan^3x+2\tan x+3=3+3\tan^2x\\\Leftrightarrow \tan^3x+2\tan x+3-3-3\tan^2x=0\\\Leftrightarrow \tan^3x-3\tan^2x+2\tan x=0\\\Leftrightarrow \tan x(\tan^2x-3\tan x+2)=0\\\Leftrightarrow \tan x(\tan x-1)(\tan x-2)=0\\\Leftrightarrow \left[\begin{array}{I}\tan x=0\\\tan x=1\\\tan x=2\end{array}\right.\\\Leftrightarrow \left[\begin{array}{I}x=k\pi\\x=\dfrac{\pi}{4}+k\pi\\x=\arctan2+k\pi.\end{array}\right.\quad(k\in\mathbb{Z})\\\text{Vậy S=}\left\{k\pi;\dfrac{\pi}{4}+k\pi;\arctan2+k\pi\Big|k\in\mathbb{Z}\right\}.\)

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