Toán Lớp 11: sinx.tan2x +1 = sinx +tan 2x ????
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: sinx.tan2x +1 = sinx +tan 2x ????
Comments ( 2 )
\quad \sin x.\tan2x + 1= \sin x + \tan2x\qquad (*)\\
ĐK:\ \cos2x \ne 0 \Leftrightarrow x \ne \dfrac{\pi}{4} + \dfrac{n\pi}{2}\\
(*) \Leftrightarrow \sin x.\tan2x – \tan2x + 1 – \sin x = 0\\
\Leftrightarrow \tan2x(\sin x – 1) – (\sin x – 1) = 0\\
\Leftrightarrow (\tan2x – 1)(\sin x – 1) =0\\
\Leftrightarrow \left[\begin{array}{l}\tan2x = 1\\\sin x = 1\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}2x = \dfrac{\pi}{4} + k\pi\\x = \dfrac{\pi}{2} + k2\pi\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x = \dfrac{\pi}{8} + k\dfrac{\pi}{2}\\x = \dfrac{\pi}{2} + k2\pi\end{array}\right.\quad (k\in\Bbb Z)\\
\text{Vậy phương trình có các họ nghiệm là}\ x =\dfrac{\pi}{8} + k\dfrac{\pi}{2}\ \text{và}\ x=\dfrac{\pi}{2} + k2\pi\ \text{với}\ k\in\Bbb Z
\end{array}\)