Toán Lớp 11: giải phương trình: a) cotx+sinx(1+tanx.tanx/2)=4
Leave a reply
Register Now
Login
Lost Password
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Toán Lớp 11: giải phương trình: a) cotx+sinx(1+tanx.tanx/2)=4
Comments ( 1 )
\cot x + \sin x\left( {1 + \tan x.\tan \dfrac{x}{2}} \right) = 4\\
\Leftrightarrow \cot x + \sin x\left( {1 + \dfrac{{\sin x.\sin \dfrac{x}{2}}}{{\cos x.\cos \dfrac{x}{2}}}} \right) = 4\\
\Leftrightarrow \cot x + \sin x.\dfrac{{\cos x.\cos \dfrac{x}{2} + \sin x.\sin \dfrac{x}{2}}}{{\cos x.\cos \dfrac{x}{2}}} = 4\\
\Leftrightarrow \cot x + \sin x.\dfrac{{\cos \left( {x – \dfrac{x}{2}} \right)}}{{\cos x.\cos \dfrac{x}{2}}} = 4\\
\Leftrightarrow \cot x + \sin x.\dfrac{{\cos \dfrac{x}{2}}}{{\cos x.\cos \dfrac{x}{2}}} = 4\\
\Leftrightarrow \cot x + \dfrac{{\sin x}}{{\cos x}} = 4\\
\Leftrightarrow \dfrac{1}{{\tan x}} + \tan x = 4\\
\Leftrightarrow {\tan ^2}x – 4\tan x + 1 = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\tan x = 2 + \sqrt 3 \\
\tan x = 2 – \sqrt 3
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \arctan \left( {2 + \sqrt 3 } \right) + k\pi ™\\
x = \arctan \left( {2 – \sqrt 3 } \right) + k\pi ™
\end{array} \right.
\end{array}$