giải pt: tan x – 2cot x +1 = 0 giúp vs ạ 02/10/2021 Bởi Melody giải pt: tan x – 2cot x +1 = 0 giúp vs ạ
\[\begin{array}{l} \tan x – 2\cot x + 1 = 0\\ DK:\,\,\,\left\{ \begin{array}{l} \cos x \ne 0\\ \sin x \ne 0 \end{array} \right. \Leftrightarrow \sin 2x \ne 0.\\ \Leftrightarrow \tan x – 2.\frac{1}{{\tan x}} + 1 = 0\\ \Leftrightarrow {\tan ^2}x + \tan x – 2 = 0\\ \Leftrightarrow \left( {\tan x – 1} \right)\left( {\tan x + 2} \right) = 0\\ \Leftrightarrow \left[ \begin{array}{l} \tan x – 1 = 0\\ \tan x + 2 = 0 \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} \tan x = 1\\ \tan x = – 2 \end{array} \right.. \end{array}\] Bình luận
$$\eqalign{ & \tan x – \cot x + 1 = 0\, \cr & DKXD:\,\left\{ \matrix{ \sin x \ne 0 \hfill \cr \cos x \ne 0 \hfill \cr} \right. \Leftrightarrow \sin 2x \ne 0 \cr & \Leftrightarrow 2x \ne k\pi \Leftrightarrow x \ne {{k\pi } \over 2}\,\,\left( {k \in Z} \right) \cr & PT \Leftrightarrow \tan x – {2 \over {\tan x}} + 1 = 0 \cr & \Leftrightarrow {\tan ^2}x + \tan x – 2 = 0 \cr & \Leftrightarrow \left[ \matrix{ \tan x = 1 \hfill \cr \tan x = – 2 \hfill \cr} \right. \Leftrightarrow \left[ \matrix{ x = {\pi \over 4} + k\pi \hfill \cr x = \arctan \left( { – 2} \right) + k\pi \hfill \cr} \right.\,\,\left( {k \in Z} \right) \cr} $$ Bình luận
\[\begin{array}{l}
\tan x – 2\cot x + 1 = 0\\
DK:\,\,\,\left\{ \begin{array}{l}
\cos x \ne 0\\
\sin x \ne 0
\end{array} \right. \Leftrightarrow \sin 2x \ne 0.\\
\Leftrightarrow \tan x – 2.\frac{1}{{\tan x}} + 1 = 0\\
\Leftrightarrow {\tan ^2}x + \tan x – 2 = 0\\
\Leftrightarrow \left( {\tan x – 1} \right)\left( {\tan x + 2} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\tan x – 1 = 0\\
\tan x + 2 = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\tan x = 1\\
\tan x = – 2
\end{array} \right..
\end{array}\]
$$\eqalign{
& \tan x – \cot x + 1 = 0\, \cr
& DKXD:\,\left\{ \matrix{
\sin x \ne 0 \hfill \cr
\cos x \ne 0 \hfill \cr} \right. \Leftrightarrow \sin 2x \ne 0 \cr
& \Leftrightarrow 2x \ne k\pi \Leftrightarrow x \ne {{k\pi } \over 2}\,\,\left( {k \in Z} \right) \cr
& PT \Leftrightarrow \tan x – {2 \over {\tan x}} + 1 = 0 \cr
& \Leftrightarrow {\tan ^2}x + \tan x – 2 = 0 \cr
& \Leftrightarrow \left[ \matrix{
\tan x = 1 \hfill \cr
\tan x = – 2 \hfill \cr} \right. \Leftrightarrow \left[ \matrix{
x = {\pi \over 4} + k\pi \hfill \cr
x = \arctan \left( { – 2} \right) + k\pi \hfill \cr} \right.\,\,\left( {k \in Z} \right) \cr} $$